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:
$\text{A}$ $\text{boat}$ $\text{rental}$ $\text{costs}$ $\text{\$50}$ $\text{for}$ $\text{2}$ $\text{hours}$ $\text{and}$ $\text{\$110}$ $\text{for}$ $\text{6}$ $\text{hours.}$ $\text{Find}$ $\text{the}$ $\text{cost}$ $\text{per}$ $\text{hour.}$