Grade 8 Algebra: Slope from Two Points

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Positive whole-number slopes

1. Find the slope:
$(1,2),\ (3,6)$
2. Find the slope:
$(0,1),\ (2,7)$
3. Find the slope:
$(2,3),\ (6,7)$
4. Find the slope:
$(1,1),\ (4,13)$
5. Find the slope:
$(0,0),\ (5,10)$
6. Find the slope:
$(3,2),\ (5,12)$
7. Find the slope:
$(2,5),\ (4,11)$
8. Find the slope:
$(1,4),\ (7,10)$

Answer Key

Level 1

1. $2$
2. $3$
3. $1$
4. $4$
5. $2$
6. $5$
7. $3$
8. $1$

Grade 8 Algebra: Slope from Two Points

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Negative and fractional slopes

1. Find the slope:
$(1,5),\ (3,1)$
2. Find the slope:
$(0,4),\ (2,-2)$
3. Find the slope:
$(2,1),\ (6,3)$
4. Find the slope:
$(-1,2),\ (3,5)$
5. Find the slope:
$(-2,-3),\ (1,3)$
6. Find the slope:
$(4,-1),\ (-2,2)$
7. Find the slope:
$(0,0),\ (3,-2)$
8. Find the slope:
$(-3,4),\ (-1,-4)$

Answer Key

Level 2

1. $-2$
2. $-3$
3. $\tfrac{1}{2}$
4. $\tfrac{3}{4}$
5. $2$
6. $-\tfrac{1}{2}$
7. $-\tfrac{2}{3}$
8. $-4$

Grade 8 Algebra: Slope from Two Points

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Zero, undefined and missing values

1. Find the slope:
$(2,5),\ (7,5)$
2. Find the slope:
$(3,1),\ (3,8)$
3. Find the slope:
$(-4,-2),\ (2,-5)$
4. Find the slope:
$(1.5,2),\ (3.5,6)$
5. Find the value of y:
$m=2:\ (1,y),\ (3,8)$
6. Find the value of x:
$m=4:\ (2,3),\ (x,11)$
7. Find the slope:
$(-6,0),\ (0,-9)$
8. Find the slope:
$(\tfrac{1}{2},1),\ (\tfrac{5}{2},4)$

Answer Key

Level 3

1. $0$
2. $\text{undefined}$
3. $-\tfrac{1}{2}$
4. $2$
5. $y=4$
6. $x=4$
7. $-\tfrac{3}{2}$
8. $\tfrac{3}{2}$

Grade 8 Algebra: Slope from Tables

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Positive rates

1. Find the rate of change:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 1 & 3 & 5 & 7 \end{array}$
2. Find the rate of change:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 0 & 4 & 8 & 12 \end{array}$
3. Find the rate of change:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 5 & 6 & 7 & 8 \end{array}$
4. Find the rate of change:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 2 & 5 & 8 & 11 \end{array}$
5. Find the rate of change:
$\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 10 & 15 & 20 & 25 \end{array}$
6. Find the rate of change:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 7 & 9 & 11 & 13 \end{array}$
7. Find the rate of change:
$\begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline y & 4 & 8 & 12 & 16 \end{array}$
8. Find the rate of change:
$\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 3 & 6 & 9 & 12 \end{array}$

Answer Key

Level 1

1. $2$
2. $4$
3. $1$
4. $3$
5. $5$
6. $2$
7. $2$
8. $3$

Grade 8 Algebra: Slope from Tables

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Negative and fractional rates

1. Find the rate of change:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 10 & 8 & 6 & 4 \end{array}$
2. Find the rate of change:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 9 & 6 & 3 & 0 \end{array}$
3. Find the rate of change:
$\begin{array}{c|cccc} x & 0 & 2 & 4 & 6 \\ \hline y & 1 & 2 & 3 & 4 \end{array}$
4. Find the rate of change:
$\begin{array}{c|cccc} x & 0 & 4 & 8 & 12 \\ \hline y & 0 & 3 & 6 & 9 \end{array}$
5. Find the rate of change:
$\begin{array}{c|cccc} x & -2 & -1 & 0 & 1 \\ \hline y & 5 & 3 & 1 & -1 \end{array}$
6. Find the rate of change:
$\begin{array}{c|cccc} x & 0 & 3 & 6 & 9 \\ \hline y & 8 & 6 & 4 & 2 \end{array}$
7. Find the rate of change:
$\begin{array}{c|cccc} x & 1 & 3 & 5 & 7 \\ \hline y & -4 & 0 & 4 & 8 \end{array}$
8. Find the rate of change:
$\begin{array}{c|cccc} x & -3 & 0 & 3 & 6 \\ \hline y & 4 & 3 & 2 & 1 \end{array}$

Answer Key

Level 2

1. $-2$
2. $-3$
3. $\tfrac{1}{2}$
4. $\tfrac{3}{4}$
5. $-2$
6. $-\tfrac{2}{3}$
7. $2$
8. $-\tfrac{1}{3}$

Grade 8 Algebra: Slope from Tables

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Constant rates and missing values

1. Is the rate of change constant? If so, find it:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 1 & 4 & 9 & 16 \end{array}$
2. Is the rate of change constant? If so, find it:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 6 & 6 & 6 & 6 \end{array}$
3. Is the rate of change constant? If so, find it:
$\begin{array}{c|cccc} x & 2 & 5 & 8 & 11 \\ \hline y & 1 & 3 & 5 & 7 \end{array}$
4. Is the rate of change constant? If so, find it:
$\begin{array}{c|cccc} x & 1 & 2 & 4 & 5 \\ \hline y & 3 & 5 & 9 & 11 \end{array}$
5. Is the rate of change constant? If so, find it:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 1 & 2 & 4 & 8 \end{array}$
6. Find the missing value (constant rate):
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 2 & 7 & ? & 17 \end{array}$
7. Find the missing value (constant rate):
$\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 20 & ? & 10 & 5 \end{array}$
8. Find the missing value (constant rate):
$\begin{array}{c|cccc} x & 0 & 2 & 4 & 6 \\ \hline y & -3 & ? & 5 & 9 \end{array}$

Answer Key

Level 3

1. $\text{not constant}$
2. $\text{constant, } 0$
3. $\text{constant, } \tfrac{2}{3}$
4. $\text{constant, } 2$
5. $\text{not constant}$
6. $12$
7. $15$
8. $1$

Grade 8 Algebra: Rate of Change and Unit Rates

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Unit rates

1. Solve:
$\text{A}$ $\text{car}$ $\text{goes}$ $\text{120}$ $\text{miles}$ $\text{in}$ $\text{2}$ $\text{hours.}$ $\text{Find}$ $\text{the}$ $\text{speed.}$
2. Solve:
$\text{5}$ $\text{pens}$ $\text{cost}$ $\text{\$15.}$ $\text{Find}$ $\text{the}$ $\text{cost}$ $\text{per}$ $\text{pen.}$
3. Solve:
$\text{Sam}$ $\text{types}$ $\text{240}$ $\text{words}$ $\text{in}$ $\text{4}$ $\text{minutes.}$ $\text{Find}$ $\text{the}$ $\text{words}$ $\text{per}$ $\text{minute.}$
4. Solve:
$\text{A}$ $\text{swimmer}$ $\text{does}$ $\text{18}$ $\text{laps}$ $\text{in}$ $\text{6}$ $\text{minutes.}$ $\text{Find}$ $\text{the}$ $\text{laps}$ $\text{per}$ $\text{minute.}$
5. Solve:
$\text{Mia}$ $\text{earns}$ $\text{\$56}$ $\text{for}$ $\text{8}$ $\text{hours}$ $\text{of}$ $\text{work.}$ $\text{Find}$ $\text{her}$ $\text{pay}$ $\text{per}$ $\text{hour.}$
6. Solve:
$\text{Leo}$ $\text{reads}$ $\text{90}$ $\text{pages}$ $\text{in}$ $\text{3}$ $\text{days.}$ $\text{Find}$ $\text{the}$ $\text{pages}$ $\text{per}$ $\text{day.}$
7. Solve:
$\text{A}$ $\text{hose}$ $\text{fills}$ $\text{20}$ $\text{gallons}$ $\text{in}$ $\text{4}$ $\text{minutes.}$ $\text{Find}$ $\text{the}$ $\text{gallons}$ $\text{per}$ $\text{minute.}$
8. Solve:
$\text{6}$ $\text{apples}$ $\text{cost}$ $\text{\$9.}$ $\text{Find}$ $\text{the}$ $\text{cost}$ $\text{per}$ $\text{apple.}$

Answer Key

Level 1

1. $60\text{ mi per h}$
2. $\$3\text{ per pen}$
3. $60\text{ words per min}$
4. $3\text{ laps per min}$
5. $\$7\text{ per h}$
6. $30\text{ pages per day}$
7. $5\text{ gal per min}$
8. $\$1.50\text{ per apple}$

Grade 8 Algebra: Rate of Change and Unit Rates

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Rate of change between two points

1. Solve:
$\text{After}$ $\text{2}$ $\text{hours}$ $\text{a}$ $\text{car}$ $\text{has}$ $\text{gone}$ $\text{100}$ $\text{miles.}$ $\text{After}$ $\text{5}$ $\text{hours}$ $\text{it}$ $\text{has}$ $\text{gone}$ $\text{250}$ $\text{miles.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$
2. Solve:
$\text{A}$ $\text{plant}$ $\text{is}$ $\text{4}$ $\text{cm}$ $\text{tall}$ $\text{on}$ $\text{day}$ $\text{1}$ $\text{and}$ $\text{10}$ $\text{cm}$ $\text{tall}$ $\text{on}$ $\text{day}$ $\text{4.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$
3. Solve:
$\text{It}$ $\text{is}$ $\text{20}$ $\text{degrees}$ $F\text{}$ $\text{at}$ $\text{6}$ $\text{am}$ $\text{and}$ $\text{8}$ $\text{degrees}$ $F\text{}$ $\text{at}$ $\text{10}$ $\text{am.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$
4. Solve:
$\text{A}$ $\text{phone}$ $\text{battery}$ $\text{is}$ $\text{at}$ $\text{90\%}$ $\text{at}$ $\text{1}$ $\text{pm}$ $\text{and}$ $\text{60\%}$ $\text{at}$ $\text{4}$ $\text{pm.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$
5. Solve:
$\text{Savings}$ $\text{are}$ $\text{\$50}$ $\text{after}$ $\text{2}$ $\text{weeks}$ $\text{and}$ $\text{\$110}$ $\text{after}$ $\text{6}$ $\text{weeks.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$
6. Solve:
$\text{A}$ $\text{tank}$ $\text{holds}$ $\text{40}$ $L\text{}$ $\text{after}$ $\text{3}$ $\text{minutes}$ $\text{and}$ $\text{16}$ $L\text{}$ $\text{after}$ $\text{9}$ $\text{minutes.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$
7. Solve:
$\text{A}$ $\text{3}$ $\text{mile}$ $\text{taxi}$ $\text{ride}$ $\text{costs}$ $\text{\$10}$ $\text{and}$ $\text{a}$ $\text{7}$ $\text{mile}$ $\text{ride}$ $\text{costs}$ $\text{\$18.}$ $\text{Find}$ $\text{the}$ $\text{cost}$ $\text{per}$ $\text{extra}$ $\text{mile.}$
8. Solve:
$\text{An}$ $\text{elevator}$ $\text{is}$ $\text{at}$ $\text{floor}$ $\text{12}$ $\text{at}$ $\text{0}$ $\text{seconds}$ $\text{and}$ $\text{at}$ $\text{floor}$ $\text{2}$ $\text{at}$ $\text{20}$ $\text{seconds.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$

Answer Key

Level 2

1. $50\text{ mi per h}$
2. $2\text{ cm per day}$
3. $-3\text{ degrees per h}$
4. $-10\%\text{ per h}$
5. $\$15\text{ per week}$
6. $-4\text{ L per min}$
7. $\$2\text{ per mi}$
8. $-0.5\text{ floors per s}$

Grade 8 Algebra: Rate of Change and Unit Rates

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Comparing and using rates

1. Solve:
$\text{Ann}$ $\text{reads}$ $\text{45}$ $\text{pages}$ $\text{in}$ $\text{1.5}$ $\text{hours.}$ $\text{Ben}$ $\text{reads}$ $\text{64}$ $\text{pages}$ $\text{in}$ $\text{2}$ $\text{hours.}$ $\text{Who}$ $\text{reads}$ $\text{faster?}$
2. Solve:
$\text{Store}$ $\text{1}$ $\text{sells}$ $\text{6}$ $\text{cans}$ $\text{for}$ $\text{\$4.50.}$ $\text{Store}$ $\text{2}$ $\text{sells}$ $\text{8}$ $\text{cans}$ $\text{for}$ $\text{\$5.60.}$ $\text{Which}$ $\text{is}$ $\text{the}$ $\text{better}$ $\text{buy?}$
3. Solve:
$\text{A}$ $\text{runner}$ $\text{goes}$ $\text{400}$ $m\text{}$ $\text{in}$ $\text{80}$ $s\text{.}$ $\text{A}$ $\text{cyclist}$ $\text{goes}$ $\text{1500}$ $m\text{}$ $\text{in}$ $\text{250}$ $s\text{.}$ $\text{Who}$ $\text{is}$ $\text{faster?}$
4. Solve:
$\text{A}$ $\text{pump}$ $\text{fills}$ $\text{180}$ $L\text{}$ $\text{in}$ $\text{12}$ $\text{minutes.}$ $\text{How}$ $\text{long}$ $\text{to}$ $\text{fill}$ $\text{300}$ $L\text{?}$
5. Solve:
$\text{A}$ $\text{car}$ $\text{uses}$ $\text{3}$ $\text{gallons}$ $\text{for}$ $\text{96}$ $\text{miles.}$ $\text{How}$ $\text{far}$ $\text{can}$ $\text{it}$ $\text{go}$ $\text{on}$ $\text{8}$ $\text{gallons?}$
6. Solve:
$\text{A}$ $\text{lake}$ $\text{drops}$ $\text{from}$ $\text{18}$ $\text{ft}$ $\text{to}$ $\text{12}$ $\text{ft}$ $\text{in}$ $\text{4}$ $\text{days.}$ $\text{Find}$ $\text{the}$ $\text{rate.}$ $\text{At}$ $\text{this}$ $\text{rate,}$ $\text{how}$ $\text{many}$ $\text{more}$ $\text{days}$ $\text{until}$ $\text{it}$ $\text{reaches}$ $\text{0}$ $\text{ft?}$
7. Solve:
$\text{Printer}$ $\text{1}$ $\text{prints}$ $\text{150}$ $\text{pages}$ $\text{in}$ $\text{5}$ $\text{minutes.}$ $\text{Printer}$ $\text{2}$ $\text{follows}$ $y\text{}$ $\text{=}$ $\text{35x,}$ $\text{where}$ $x\text{}$ $\text{is}$ $\text{minutes.}$ $\text{Which}$ $\text{is}$ $\text{faster?}$
8. Solve:
$\text{A}$ $\text{hiker}$ $\text{climbs}$ $\text{from}$ $\text{1200}$ $m\text{}$ $\text{to}$ $\text{2000}$ $m\text{}$ $\text{in}$ $\text{4}$ $\text{hours.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{climb.}$

Answer Key

Level 3

1. $\text{Ben (32 vs 30 pages per h)}$
2. $\text{Store 2 (\$0.70 vs \$0.75 per can)}$
3. $\text{cyclist (6 vs 5 m per s)}$
4. $20\text{ min}$
5. $256\text{ mi}$
6. $-1.5\text{ ft per day; 8 more days}$
7. $\text{Printer 2 (35 vs 30 pages per min)}$
8. $200\text{ m per h}$

Grade 8 Algebra: Word Problems: Slope and Rate of Change

Name: ______________________Date: ____________Score: ____ / 8

Level 1

What the rate means

1. Solve:
$\text{Tickets}$ $\text{cost}$ $y\text{}$ $\text{=}$ $\text{8x}$ $\text{dollars}$ $\text{for}$ $x\text{}$ $\text{tickets.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{and}$ $\text{say}$ $\text{what}$ $\text{it}$ $\text{means.}$
2. Solve:
$\text{Pay}$ $\text{is}$ $y\text{}$ $\text{=}$ $\text{12x}$ $\text{dollars}$ $\text{for}$ $x\text{}$ $\text{hours.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{and}$ $\text{say}$ $\text{what}$ $\text{it}$ $\text{means.}$
3. Solve:
$\text{A}$ $\text{train}$ $\text{goes}$ $y\text{}$ $\text{=}$ $\text{50x}$ $\text{miles}$ $\text{in}$ $x\text{}$ $\text{hours.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{and}$ $\text{say}$ $\text{what}$ $\text{it}$ $\text{means.}$
4. Solve:
$\text{A}$ $\text{pizza}$ $\text{costs}$ $y\text{}$ $\text{=}$ $\text{3x}$ $\text{+}$ $\text{5}$ $\text{dollars}$ $\text{with}$ $x\text{}$ $\text{toppings.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{and}$ $\text{say}$ $\text{what}$ $\text{it}$ $\text{means.}$
5. Solve:
$\text{A}$ $\text{plant}$ $\text{is}$ $y\text{}$ $\text{=}$ $\text{2x}$ $\text{+}$ $\text{10}$ $\text{cm}$ $\text{tall}$ $\text{after}$ $x\text{}$ $\text{weeks.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{and}$ $\text{say}$ $\text{what}$ $\text{it}$ $\text{means.}$
6. Solve:
$\text{A}$ $\text{tank}$ $\text{has}$ $y\text{}$ $\text{=}$ $\text{-4x}$ $\text{+}$ $\text{40}$ $\text{liters}$ $\text{after}$ $x\text{}$ $\text{minutes.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{and}$ $\text{say}$ $\text{what}$ $\text{it}$ $\text{means.}$
7. Solve:
$\text{Savings}$ $\text{are}$ $y\text{}$ $\text{=}$ $\text{25x}$ $\text{+}$ $\text{100}$ $\text{dollars}$ $\text{after}$ $x\text{}$ $\text{weeks.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{and}$ $\text{say}$ $\text{what}$ $\text{it}$ $\text{means.}$
8. Solve:
$\text{A}$ $\text{battery}$ $\text{is}$ $\text{at}$ $y\text{}$ $\text{=}$ $\text{-5x}$ $\text{+}$ $\text{60}$ $\text{percent}$ $\text{after}$ $x\text{}$ $\text{hours.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{and}$ $\text{say}$ $\text{what}$ $\text{it}$ $\text{means.}$

Answer Key

Level 1

1. $8:\ \$8\text{ per ticket}$
2. $12:\ \$12\text{ per hour}$
3. $50:\ 50\text{ mi per hour}$
4. $3:\ \$3\text{ per topping}$
5. $2:\ \text{grows 2 cm per week}$
6. $-4:\ \text{loses 4 L per min}$
7. $25:\ \text{saves \$25 per week}$
8. $-5:\ \text{drops 5\% per hour}$

Grade 8 Algebra: Word Problems: Slope and Rate of Change

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Slope from two points in context

1. Solve:
$\text{A}$ $\text{ramp}$ $\text{rises}$ $\text{3}$ $\text{ft}$ $\text{over}$ $\text{a}$ $\text{run}$ $\text{of}$ $\text{12}$ $\text{ft.}$ $\text{Find}$ $\text{its}$ $\text{slope.}$
2. Solve:
$\text{A}$ $\text{roof}$ $\text{rises}$ $\text{6}$ $\text{ft}$ $\text{over}$ $\text{a}$ $\text{run}$ $\text{of}$ $\text{15}$ $\text{ft.}$ $\text{Find}$ $\text{its}$ $\text{slope.}$
3. Solve:
$\text{A}$ $\text{road}$ $\text{climbs}$ $\text{40}$ $m\text{}$ $\text{over}$ $\text{a}$ $\text{run}$ $\text{of}$ $\text{800}$ $m\text{.}$ $\text{Find}$ $\text{its}$ $\text{slope.}$
4. Solve:
$\text{A}$ $\text{slide}$ $\text{drops}$ $\text{8}$ $\text{ft}$ $\text{over}$ $\text{a}$ $\text{run}$ $\text{of}$ $\text{10}$ $\text{ft.}$ $\text{Find}$ $\text{its}$ $\text{slope.}$
5. Solve:
$\text{A}$ $\text{gym}$ $\text{costs}$ $\text{\$70}$ $\text{for}$ $\text{2}$ $\text{months}$ $\text{and}$ $\text{\$145}$ $\text{for}$ $\text{5}$ $\text{months.}$ $\text{Find}$ $\text{the}$ $\text{cost}$ $\text{per}$ $\text{month.}$
6. Solve:
$\text{A}$ $\text{candle}$ $\text{is}$ $\text{20}$ $\text{cm}$ $\text{tall}$ $\text{after}$ $\text{1}$ $\text{hour}$ $\text{and}$ $\text{14}$ $\text{cm}$ $\text{tall}$ $\text{after}$ $\text{4}$ $\text{hours.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$
7. Solve:
$\text{An}$ $\text{elevator}$ $\text{goes}$ $\text{from}$ $\text{300}$ $\text{ft}$ $\text{to}$ $\text{60}$ $\text{ft}$ $\text{in}$ $\text{30}$ $\text{seconds.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$
8. Solve:
$\text{A}$ $\text{boat}$ $\text{rental}$ $\text{costs}$ $\text{\$50}$ $\text{for}$ $\text{2}$ $\text{hours}$ $\text{and}$ $\text{\$110}$ $\text{for}$ $\text{6}$ $\text{hours.}$ $\text{Find}$ $\text{the}$ $\text{cost}$ $\text{per}$ $\text{hour.}$

Answer Key

Level 2

1. $\tfrac{1}{4}$
2. $\tfrac{2}{5}$
3. $\tfrac{1}{20}$
4. $-\tfrac{4}{5}$
5. $\$25\text{ per month}$
6. $-2\text{ cm per h}$
7. $-8\text{ ft per s}$
8. $\$15\text{ per h}$

Grade 8 Algebra: Word Problems: Slope and Rate of Change

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Using and comparing slopes

1. Solve:
$\text{A}$ $\text{safe}$ $\text{ramp}$ $\text{has}$ $\text{a}$ $\text{slope}$ $\text{of}$ $\text{at}$ $\text{most}$ $\text{1/12.}$ $\text{If}$ $\text{it}$ $\text{rises}$ $\text{2}$ $\text{ft,}$ $\text{what}$ $\text{is}$ $\text{the}$ $\text{shortest}$ $\text{run?}$
2. Solve:
$\text{A}$ $\text{pool}$ $\text{has}$ $\text{500}$ $\text{gallons}$ $\text{and}$ $\text{drains}$ $\text{at}$ $\text{25}$ $\text{gallons}$ $\text{per}$ $\text{minute.}$ $\text{How}$ $\text{much}$ $\text{is}$ $\text{left}$ $\text{after}$ $\text{8}$ $\text{minutes?}$
3. Solve:
$\text{A}$ $\text{hill}$ $\text{has}$ $\text{a}$ $\text{slope}$ $\text{of}$ $\text{0.15.}$ $\text{How}$ $\text{much}$ $\text{does}$ $\text{it}$ $\text{rise}$ $\text{over}$ $\text{a}$ $\text{run}$ $\text{of}$ $\text{200}$ $m\text{?}$
4. Solve:
$\text{Plan}$ $\text{1}$ $\text{costs}$ $\text{\$20}$ $\text{plus}$ $\text{\$5}$ $\text{per}$ $\text{month.}$ $\text{Plan}$ $\text{2}$ $\text{costs}$ $\text{\$10}$ $\text{per}$ $\text{month.}$ $\text{Which}$ $\text{cost}$ $\text{grows}$ $\text{faster?}$ $\text{After}$ $\text{how}$ $\text{many}$ $\text{months}$ $\text{are}$ $\text{they}$ $\text{equal?}$
5. Solve:
$\text{Snow}$ $\text{is}$ $\text{3}$ $\text{in}$ $\text{deep}$ $\text{at}$ $\text{2}$ $\text{pm}$ $\text{and}$ $\text{9}$ $\text{in}$ $\text{deep}$ $\text{at}$ $\text{5}$ $\text{pm.}$ $\text{At}$ $\text{this}$ $\text{rate,}$ $\text{how}$ $\text{deep}$ $\text{is}$ $\text{it}$ $\text{at}$ $\text{7}$ $\text{pm?}$
6. Solve:
$\text{A}$ $\text{car}$ $\text{is}$ $\text{worth}$ $\text{\$24000}$ $\text{new}$ $\text{and}$ $\text{\$18000}$ $\text{after}$ $\text{3}$ $\text{years.}$ $\text{Find}$ $\text{the}$ $\text{rate.}$ $\text{What}$ $\text{is}$ $\text{it}$ $\text{worth}$ $\text{after}$ $\text{5}$ $\text{years?}$
7. Solve:
$\text{The}$ $\text{top}$ $\text{of}$ $\text{a}$ $\text{ladder}$ $\text{is}$ $\text{12}$ $\text{ft}$ $\text{up}$ $\text{a}$ $\text{wall}$ $\text{and}$ $\text{its}$ $\text{base}$ $\text{is}$ $\text{5}$ $\text{ft}$ $\text{from}$ $\text{the}$ $\text{wall.}$ $\text{Find}$ $\text{the}$ $\text{slope}$ $\text{of}$ $\text{the}$ $\text{ladder.}$
8. Solve:
$\text{Ramp}$ $\text{1}$ $\text{rises}$ $\text{2}$ $\text{ft}$ $\text{over}$ $\text{10}$ $\text{ft.}$ $\text{Ramp}$ $\text{2}$ $\text{rises}$ $\text{3}$ $\text{ft}$ $\text{over}$ $\text{12}$ $\text{ft.}$ $\text{Which}$ $\text{is}$ $\text{steeper?}$

Answer Key

Level 3

1. $24\text{ ft}$
2. $300\text{ gal}$
3. $30\text{ m}$
4. $\text{Plan 2; 4 months}$
5. $13\text{ in}$
6. $-\$2000\text{ per year; } \$14000$
7. $\tfrac{12}{5}$
8. $\text{Ramp 2 } (\tfrac{1}{4}>\tfrac{1}{5})$

Grade 8 Algebra: Comparing Unit Rates: Tables, Equations and Points

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Tables and equations through the origin

1. Which has the greater unit rate:
$\begin{array}{ll} \textbf{A:} & y = 3x \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 4 & 8 & 12 & 16 \end{array} \end{array}$
2. Which has the greater unit rate:
$\begin{array}{ll} \textbf{A:} & y = 5x \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 0 & 6 & 12 & 18 \end{array} \end{array}$
3. Which has the greater unit rate:
$\begin{array}{ll} \textbf{A:} & y = 7x \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 6 & 12 & 18 & 24 \end{array} \end{array}$
4. Which has the greater unit rate:
$\begin{array}{ll} \textbf{A:} & \begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline y & 10 & 20 & 30 & 40 \end{array} \\[14pt] \textbf{B:} & y = 4x \end{array}$
5. Which has the greater unit rate:
$\begin{array}{ll} \textbf{A:} & y = 2x \\[14pt] \textbf{B:} & y = 2.5x \end{array}$
6. Which has the greater unit rate:
$\begin{array}{ll} \textbf{A:} & \begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 9 & 18 & 27 & 36 \end{array} \\[14pt] \textbf{B:} & y = 8x \end{array}$
7. Which has the greater unit rate:
$\begin{array}{ll} \textbf{A:} & y = 10x \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline y & 22 & 44 & 66 & 88 \end{array} \end{array}$
8. Which has the greater unit rate:
$\begin{array}{ll} \textbf{A:} & \begin{array}{c|cccc} x & 3 & 6 & 9 & 12 \\ \hline y & 12 & 24 & 36 & 48 \end{array} \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 5 & 10 & 15 & 20 \\ \hline y & 15 & 30 & 45 & 60 \end{array} \end{array}$

Answer Key

Level 1

1. $B\ (4 > 3)$
2. $B\ (6 > 5)$
3. $A\ (7 > 6)$
4. $A\ (5 > 4)$
5. $B\ (2.5 > 2)$
6. $A\ (9 > 8)$
7. $B\ (11 > 10)$
8. $A\ (4 > 3)$

Grade 8 Algebra: Comparing Unit Rates: Tables, Equations and Points

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Tables, equations and two points

1. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & (1, 4),\ (3, 10) \\[14pt] \textbf{B:} & y = 2x + 5 \end{array}$
2. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & (0, 2),\ (4, 22) \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 1 & 7 & 13 & 19 \end{array} \end{array}$
3. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & y = 1.5x \\[14pt] \textbf{B:} & (2, 4),\ (6, 10) \end{array}$
4. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & \begin{array}{c|cccc} x & 0 & 2 & 4 & 6 \\ \hline y & 3 & 7 & 11 & 15 \end{array} \\[14pt] \textbf{B:} & (1, 1),\ (4, 10) \end{array}$
5. Which decreases faster:
$\begin{array}{ll} \textbf{A:} & y = -2x + 8 \\[14pt] \textbf{B:} & (0, 12),\ (4, 0) \end{array}$
6. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & (2, 5),\ (6, 7) \\[14pt] \textbf{B:} & y = \tfrac{1}{3}x + 4 \end{array}$
7. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & \begin{array}{c|cccc} x & 1 & 3 & 5 & 7 \\ \hline y & 4 & 10 & 16 & 22 \end{array} \\[14pt] \textbf{B:} & (2, 9),\ (5, 21) \end{array}$
8. Which has the greater rate of change:
$\begin{array}{ll} \textbf{A:} & (-1, 2),\ (3, 14) \\[14pt] \textbf{B:} & y = 3x - 1 \end{array}$

Answer Key

Level 2

1. $A\ (3 > 2)$
2. $B\ (6 > 5)$
3. $\text{Same } (1.5)$
4. $B\ (3 > 2)$
5. $B\ (-3\text{ vs }-2)$
6. $A\ (\tfrac{1}{2} > \tfrac{1}{3})$
7. $B\ (4 > 3)$
8. $\text{Same } (3)$

Grade 8 Algebra: Comparing Unit Rates: Tables, Equations and Points

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Comparing rates in context

1. Which car is faster (x = hours, y = miles):
$\begin{array}{ll} \textbf{A:} & y = 55x \\[14pt] \textbf{B:} & (2, 120),\ (5, 300) \end{array}$
2. Which worker earns more per hour (x = hours, y = dollars):
$\begin{array}{ll} \textbf{A:} & y = 14x + 20 \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline y & 30 & 60 & 90 & 120 \end{array} \end{array}$
3. Which plan costs less per GB (x = GB, y = dollars):
$\begin{array}{ll} \textbf{A:} & (2, 13),\ (6, 25) \\[14pt] \textbf{B:} & y = 3.5x + 5 \end{array}$
4. Which tank drains faster (x = minutes, y = liters):
$\begin{array}{ll} \textbf{A:} & y = -6x + 90 \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 0 & 5 & 10 & 15 \\ \hline y & 100 & 75 & 50 & 25 \end{array} \end{array}$
5. Which printer is faster (x = minutes, y = pages):
$\begin{array}{ll} \textbf{A:} & (3, 45),\ (7, 105) \\[14pt] \textbf{B:} & y = 16x \end{array}$
6. Which is the better buy (x = pounds, y = dollars):
$\begin{array}{ll} \textbf{A:} & \begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline y & 7 & 14 & 21 & 28 \end{array} \\[14pt] \textbf{B:} & (3, 12),\ (5, 20) \end{array}$
7. Which runner is faster (x = minutes, y = meters):
$\begin{array}{ll} \textbf{A:} & \begin{array}{c|cccc} x & 0 & 2 & 4 & 6 \\ \hline y & 0 & 400 & 800 & 1200 \end{array} \\[14pt] \textbf{B:} & (1, 180),\ (4, 720) \end{array}$
8. Which candle burns faster (x = hours, y = cm tall):
$\begin{array}{ll} \textbf{A:} & y = -1.5x + 20 \\[14pt] \textbf{B:} & (2, 16),\ (6, 8) \end{array}$

Answer Key

Level 3

1. $B\ (60 > 55\text{ mph})$
2. $B\ (\$15 > \$14)$
3. $A\ (\$3 < \$3.50)$
4. $A\ (6 > 5\text{ L/min})$
5. $B\ (16 > 15)$
6. $A\ (\$3.50 < \$4)$
7. $A\ (200 > 180\text{ m/min})$
8. $B\ (2 > 1.5\text{ cm/h})$

Grade 8 Algebra: Rate of Change from Two Points on a Graph

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Positive whole-number slopes

1. Find the rate of change (slope):
2. Find the rate of change (slope):
3. Find the rate of change (slope):
4. Find the rate of change (slope):
5. Find the rate of change (slope):
6. Find the rate of change (slope):
7. Find the rate of change (slope):
8. Find the rate of change (slope):

Answer Key

Level 1

1. $2$
2. $3$
3. $1$
4. $4$
5. $2$
6. $3$
7. $2$
8. $1$

Grade 8 Algebra: Rate of Change from Two Points on a Graph

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Negative, fraction, zero and undefined slopes

1. Find the rate of change (slope):
2. Find the rate of change (slope):
3. Find the rate of change (slope):
4. Find the rate of change (slope):
5. Find the rate of change (slope):
6. Find the rate of change (slope):
7. Find the rate of change (slope):
8. Find the rate of change (slope):

Answer Key

Level 2

1. $-2$
2. $-2$
3. $\tfrac{1}{2}$
4. $\tfrac{2}{3}$
5. $-\tfrac{3}{4}$
6. $0$
7. $\text{undefined}$
8. $-1$

Grade 8 Algebra: Rate of Change from Two Points on a Graph

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Graphs in context

1. Rate of change (x = hours, y = miles walked):
2. Rate of change (x = weeks, y = plant height in cm):
3. Rate of change (x = minutes, y = liters left):
4. Rate of change (x = tickets, y = dollars):
5. Rate of change (x = days, y = gallons of water):
6. Rate of change (x = hours, y = inches of snow):
7. Find the slope, then the y-intercept:
8. Find the slope, then the y-intercept:

Answer Key

Level 3

1. $2\text{ mi/h}$
2. $1\text{ cm/week}$
3. $-2\text{ L/min}$
4. $\$2\text{ per ticket}$
5. $-\tfrac{2}{3}\text{ gal/day}$
6. $\tfrac{1}{2}\text{ in/h}$
7. $\tfrac{3}{2},\ b = 4$
8. $-\tfrac{4}{3},\ b = 1$