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Linear Functions: Classroom Packet

Grade 8 Algebra: Slope-Intercept Form

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Reading m and b

  1. 1. Find the slope m and y-intercept b:
    y=2x+3y = 2x + 3
  2. 2. Find the slope m and y-intercept b:
    y=5x−1y = 5x - 1
  3. 3. Find the slope m and y-intercept b:
    y=−3x+4y = -3x + 4
  4. 4. Find the slope m and y-intercept b:
    y=x+7y = x + 7
  5. 5. Find the slope m and y-intercept b:
    y=−x−2y = -x - 2
  6. 6. Find the slope m and y-intercept b:
    y=4xy = 4x
  7. 7. Find the slope m and y-intercept b:
    y=6x−5y = 6x - 5
  8. 8. Find the slope m and y-intercept b:
    y=−2x+9y = -2x + 9

Answer Key

Level 1

  1. 1. m=2, b=3m = 2,\ b = 3
  2. 2. m=5, b=−1m = 5,\ b = -1
  3. 3. m=−3, b=4m = -3,\ b = 4
  4. 4. m=1, b=7m = 1,\ b = 7
  5. 5. m=−1, b=−2m = -1,\ b = -2
  6. 6. m=4, b=0m = 4,\ b = 0
  7. 7. m=6, b=−5m = 6,\ b = -5
  8. 8. m=−2, b=9m = -2,\ b = 9

Grade 8 Algebra: Slope-Intercept Form

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Fractions and rearranged forms

  1. 1. Find the slope m and y-intercept b:
    y=12x+6y = \tfrac{1}{2}x + 6
  2. 2. Find the slope m and y-intercept b:
    y=−34x−2y = -\tfrac{3}{4}x - 2
  3. 3. Find the slope m and y-intercept b:
    y=8−3xy = 8 - 3x
  4. 4. Find the slope m and y-intercept b:
    y=−xy = -x
  5. 5. Find the slope m and y-intercept b:
    y=5y = 5
  6. 6. Find the slope m and y-intercept b:
    y=23xy = \tfrac{2}{3}x
  7. 7. Find the slope m and y-intercept b:
    y=−4+15xy = -4 + \tfrac{1}{5}x
  8. 8. Find the slope m and y-intercept b:
    y=0.5x−1.5y = 0.5x - 1.5

Answer Key

Level 2

  1. 1. m=12, b=6m = \tfrac{1}{2},\ b = 6
  2. 2. m=−34, b=−2m = -\tfrac{3}{4},\ b = -2
  3. 3. m=−3, b=8m = -3,\ b = 8
  4. 4. m=−1, b=0m = -1,\ b = 0
  5. 5. m=0, b=5m = 0,\ b = 5
  6. 6. m=23, b=0m = \tfrac{2}{3},\ b = 0
  7. 7. m=15, b=−4m = \tfrac{1}{5},\ b = -4
  8. 8. m=12, b=−32m = \tfrac{1}{2},\ b = -\tfrac{3}{2}

Grade 8 Algebra: Slope-Intercept Form

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Rewriting into y = mx + b

  1. 1. Write in slope-intercept form, then give m and b:
    2x+y=72x + y = 7
  2. 2. Write in slope-intercept form, then give m and b:
    y−4x=1y - 4x = 1
  3. 3. Write in slope-intercept form, then give m and b:
    3x+3y=123x + 3y = 12
  4. 4. Write in slope-intercept form, then give m and b:
    2y=6x−82y = 6x - 8
  5. 5. Write in slope-intercept form, then give m and b:
    4x−2y=104x - 2y = 10
  6. 6. Write in slope-intercept form, then give m and b:
    x+2y=6x + 2y = 6
  7. 7. Write in slope-intercept form, then give m and b:
    3x−4y=83x - 4y = 8
  8. 8. Write in slope-intercept form, then give m and b:
    5y+10=2x5y + 10 = 2x

Answer Key

Level 3

  1. 1. y=−2x+7, m=−2, b=7y = -2x + 7,\ m = -2,\ b = 7
  2. 2. y=4x+1, m=4, b=1y = 4x + 1,\ m = 4,\ b = 1
  3. 3. y=−x+4, m=−1, b=4y = -x + 4,\ m = -1,\ b = 4
  4. 4. y=3x−4, m=3, b=−4y = 3x - 4,\ m = 3,\ b = -4
  5. 5. y=2x−5, m=2, b=−5y = 2x - 5,\ m = 2,\ b = -5
  6. 6. y=−12x+3, m=−12, b=3y = -\tfrac{1}{2}x + 3,\ m = -\tfrac{1}{2},\ b = 3
  7. 7. y=34x−2, m=34, b=−2y = \tfrac{3}{4}x - 2,\ m = \tfrac{3}{4},\ b = -2
  8. 8. y=25x−2, m=25, b=−2y = \tfrac{2}{5}x - 2,\ m = \tfrac{2}{5},\ b = -2

Grade 8 Algebra: Writing Equations of Lines

Name: ______________________Date: ____________Score: ____ / 8

Level 1

From slope and y-intercept

Directions: Write the equation of each line in the form y=mx+b{y = mx + b}.

  1. 1.
    m=3, b=2m = 3,\ b = 2
  2. 2.
    m=−2, b=5m = -2,\ b = 5
  3. 3.
    m=4, b=−1m = 4,\ b = -1
  4. 4.
    m=1, b=−6m = 1,\ b = -6
  5. 5.
    m=−5, b=0m = -5,\ b = 0
  6. 6.
    m=12, b=3m = \tfrac{1}{2},\ b = 3
  7. 7.
    m=−1, b=8m = -1,\ b = 8
  8. 8.
    m=0, b=−4m = 0,\ b = -4

Answer Key

Level 1

  1. 1. y=3x+2y = 3x + 2
  2. 2. y=−2x+5y = -2x + 5
  3. 3. y=4x−1y = 4x - 1
  4. 4. y=x−6y = x - 6
  5. 5. y=−5xy = -5x
  6. 6. y=12x+3y = \tfrac{1}{2}x + 3
  7. 7. y=−x+8y = -x + 8
  8. 8. y=−4y = -4

Grade 8 Algebra: Writing Equations of Lines

Name: ______________________Date: ____________Score: ____ / 8

Level 2

From slope and a point

Directions: Write the equation of each line in the form y=mx+b{y = mx + b}.

  1. 1.
    m=2, through (1,5)m = 2,\ \text{through } (1, 5)
  2. 2.
    m=3, through (2,4)m = 3,\ \text{through } (2, 4)
  3. 3.
    m=−1, through (3,1)m = -1,\ \text{through } (3, 1)
  4. 4.
    m=−4, through (1,−2)m = -4,\ \text{through } (1, -2)
  5. 5.
    m=5, through (−1,0)m = 5,\ \text{through } (-1, 0)
  6. 6.
    m=12, through (4,7)m = \tfrac{1}{2},\ \text{through } (4, 7)
  7. 7.
    m=−23, through (3,1)m = -\tfrac{2}{3},\ \text{through } (3, 1)
  8. 8.
    m=0, through (5,−3)m = 0,\ \text{through } (5, -3)

Answer Key

Level 2

  1. 1. y=2x+3y = 2x + 3
  2. 2. y=3x−2y = 3x - 2
  3. 3. y=−x+4y = -x + 4
  4. 4. y=−4x+2y = -4x + 2
  5. 5. y=5x+5y = 5x + 5
  6. 6. y=12x+5y = \tfrac{1}{2}x + 5
  7. 7. y=−23x+3y = -\tfrac{2}{3}x + 3
  8. 8. y=−3y = -3

Grade 8 Algebra: Writing Equations of Lines

Name: ______________________Date: ____________Score: ____ / 8

Level 3

From two points

Directions: Write the equation of each line in the form y=mx+b{y = mx + b}.

  1. 1.
    (0,1) and (2,7)(0, 1) \text{ and } (2, 7)
  2. 2.
    (1,3) and (3,7)(1, 3) \text{ and } (3, 7)
  3. 3.
    (2,5) and (4,1)(2, 5) \text{ and } (4, 1)
  4. 4.
    (−1,−4) and (2,5)(-1, -4) \text{ and } (2, 5)
  5. 5.
    (3,2) and (6,4)(3, 2) \text{ and } (6, 4)
  6. 6.
    (−2,6) and (2,4)(-2, 6) \text{ and } (2, 4)
  7. 7.
    (1,−1) and (5,−1)(1, -1) \text{ and } (5, -1)
  8. 8.
    (−3,−5) and (1,3)(-3, -5) \text{ and } (1, 3)

Answer Key

Level 3

  1. 1. y=3x+1y = 3x + 1
  2. 2. y=2x+1y = 2x + 1
  3. 3. y=−2x+9y = -2x + 9
  4. 4. y=3x−1y = 3x - 1
  5. 5. y=23xy = \tfrac{2}{3}x
  6. 6. y=−12x+5y = -\tfrac{1}{2}x + 5
  7. 7. y=−1y = -1
  8. 8. y=2x+1y = 2x + 1

Grade 8 Algebra: Writing Equations from Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Positive slopes, y-intercept marked

  1. 1. Write the equation of the line shown:
    1122334455667788xy
  2. 2. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  3. 3. Write the equation of the line shown:
    1122334455667788xy
  4. 4. Write the equation of the line shown:
    1122334455667788xy
  5. 5. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  6. 6. Write the equation of the line shown:
    1122334455667788xy
  7. 7. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  8. 8. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−11122334455xy

Answer Key

Level 1

  1. 1. y=2x+1y = 2x + 1
  2. 2. y=3x−2y = 3x - 2
  3. 3. y=2xy = 2x
  4. 4. y=x+3y = x + 3
  5. 5. y=2x−4y = 2x - 4
  6. 6. y=2x+2y = 2x + 2
  7. 7. y=x−1y = x - 1
  8. 8. y=4x−3y = 4x - 3

Grade 8 Algebra: Writing Equations from Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Negative, fraction and zero slopes

  1. 1. Write the equation of the line shown:
    1122334455667788xy
  2. 2. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  3. 3. Write the equation of the line shown:
    1122334455667788xy
  4. 4. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  5. 5. Write the equation of the line shown:
    1122334455667788xy
  6. 6. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  7. 7. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  8. 8. Write the equation of the line shown:
    1122334455667788xy

Answer Key

Level 2

  1. 1. y=−2x+4y = -2x + 4
  2. 2. y=−3x+1y = -3x + 1
  3. 3. y=12x+2y = \tfrac{1}{2}x + 2
  4. 4. y=23x−1y = \tfrac{2}{3}x - 1
  5. 5. y=−34x+3y = -\tfrac{3}{4}x + 3
  6. 6. y=−23xy = -\tfrac{2}{3}x
  7. 7. y=−2y = -2
  8. 8. y=−2x+5y = -2x + 5

Grade 8 Algebra: Writing Equations from Graphs

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Reading two points anywhere on the line

  1. 1. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  2. 2. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  3. 3. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  4. 4. Write the equation of the line shown:
    −6−6−5−5−4−4−3−3−2−2−1−11122334455xy
  5. 5. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  6. 6. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  7. 7. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  8. 8. Write the equation of the line shown:
    −5−5−4−4−3−3−2−2−1−1112233445566xy

Answer Key

Level 3

  1. 1. y=12xy = \tfrac{1}{2}x
  2. 2. y=−23x+2y = -\tfrac{2}{3}x + 2
  3. 3. y=12x−1y = \tfrac{1}{2}x - 1
  4. 4. y=3x−2y = 3x - 2
  5. 5. y=−34x−1y = -\tfrac{3}{4}x - 1
  6. 6. y=−12x+2y = -\tfrac{1}{2}x + 2
  7. 7. y=23x−2y = \tfrac{2}{3}x - 2
  8. 8. y=2x+3y = 2x + 3

Grade 8 Algebra: Linear Functions from Tables

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Tables starting at x = 0

  1. 1. Write an equation for the table:
    x0123y1357\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 1 & 3 & 5 & 7 \end{array}
  2. 2. Write an equation for the table:
    x0123y0369\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 0 & 3 & 6 & 9 \end{array}
  3. 3. Write an equation for the table:
    x0123y4567\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 4 & 5 & 6 & 7 \end{array}
  4. 4. Write an equation for the table:
    x0123y−23813\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & -2 & 3 & 8 & 13 \end{array}
  5. 5. Write an equation for the table:
    x0123y371115\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 3 & 7 & 11 & 15 \end{array}
  6. 6. Write an equation for the table:
    x0123y6543\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 6 & 5 & 4 & 3 \end{array}
  7. 7. Write an equation for the table:
    x0123y531−1\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 5 & 3 & 1 & -1 \end{array}
  8. 8. Write an equation for the table:
    x0123y0102030\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 0 & 10 & 20 & 30 \end{array}

Answer Key

Level 1

  1. 1. y=2x+1y = 2x + 1
  2. 2. y=3xy = 3x
  3. 3. y=x+4y = x + 4
  4. 4. y=5x−2y = 5x - 2
  5. 5. y=4x+3y = 4x + 3
  6. 6. y=−x+6y = -x + 6
  7. 7. y=−2x+5y = -2x + 5
  8. 8. y=10xy = 10x

Grade 8 Algebra: Linear Functions from Tables

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Tables with other starting values

  1. 1. Write an equation for the table:
    x1234y57911\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 5 & 7 & 9 & 11 \end{array}
  2. 2. Write an equation for the table:
    x2468y5111723\begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline y & 5 & 11 & 17 & 23 \end{array}
  3. 3. Write an equation for the table:
    x−1012y52−1−4\begin{array}{c|cccc} x & -1 & 0 & 1 & 2 \\ \hline y & 5 & 2 & -1 & -4 \end{array}
  4. 4. Write an equation for the table:
    x1357y−22610\begin{array}{c|cccc} x & 1 & 3 & 5 & 7 \\ \hline y & -2 & 2 & 6 & 10 \end{array}
  5. 5. Write an equation for the table:
    x0246y1234\begin{array}{c|cccc} x & 0 & 2 & 4 & 6 \\ \hline y & 1 & 2 & 3 & 4 \end{array}
  6. 6. Write an equation for the table:
    x−2024y20−2−4\begin{array}{c|cccc} x & -2 & 0 & 2 & 4 \\ \hline y & 2 & 0 & -2 & -4 \end{array}
  7. 7. Write an equation for the table:
    x36912y3456\begin{array}{c|cccc} x & 3 & 6 & 9 & 12 \\ \hline y & 3 & 4 & 5 & 6 \end{array}
  8. 8. Write an equation for the table:
    x1234y62−2−6\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 6 & 2 & -2 & -6 \end{array}

Answer Key

Level 2

  1. 1. y=2x+3y = 2x + 3
  2. 2. y=3x−1y = 3x - 1
  3. 3. y=−3x+2y = -3x + 2
  4. 4. y=2x−4y = 2x - 4
  5. 5. y=12x+1y = \tfrac{1}{2}x + 1
  6. 6. y=−xy = -x
  7. 7. y=13x+2y = \tfrac{1}{3}x + 2
  8. 8. y=−4x+10y = -4x + 10

Grade 8 Algebra: Linear Functions from Tables

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Fractions and nonlinear tables

  1. 1. Is this a linear function? If yes, write its equation:
    x0369y1357\begin{array}{c|cccc} x & 0 & 3 & 6 & 9 \\ \hline y & 1 & 3 & 5 & 7 \end{array}
  2. 2. Is this a linear function? If yes, write its equation:
    x0123y1248\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 1 & 2 & 4 & 8 \end{array}
  3. 3. Is this a linear function? If yes, write its equation:
    x−2024y741−2\begin{array}{c|cccc} x & -2 & 0 & 2 & 4 \\ \hline y & 7 & 4 & 1 & -2 \end{array}
  4. 4. Is this a linear function? If yes, write its equation:
    x1234y14916\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 1 & 4 & 9 & 16 \end{array}
  5. 5. Is this a linear function? If yes, write its equation:
    x5101520y−1135\begin{array}{c|cccc} x & 5 & 10 & 15 & 20 \\ \hline y & -1 & 1 & 3 & 5 \end{array}
  6. 6. Is this a linear function? If yes, write its equation:
    x−4−202y−7−4−12\begin{array}{c|cccc} x & -4 & -2 & 0 & 2 \\ \hline y & -7 & -4 & -1 & 2 \end{array}
  7. 7. Is this a linear function? If yes, write its equation:
    x0123y5568\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 5 & 5 & 6 & 8 \end{array}
  8. 8. Is this a linear function? If yes, write its equation:
    x14710y71−5−11\begin{array}{c|cccc} x & 1 & 4 & 7 & 10 \\ \hline y & 7 & 1 & -5 & -11 \end{array}

Answer Key

Level 3

  1. 1. y=23x+1y = \tfrac{2}{3}x + 1
  2. 2. No (not a constant rate)\text{No (not a constant rate)}
  3. 3. y=−32x+4y = -\tfrac{3}{2}x + 4
  4. 4. No (not a constant rate)\text{No (not a constant rate)}
  5. 5. y=25x−3y = \tfrac{2}{5}x - 3
  6. 6. y=32x−1y = \tfrac{3}{2}x - 1
  7. 7. No (not a constant rate)\text{No (not a constant rate)}
  8. 8. y=−2x+9y = -2x + 9

Grade 8 Algebra: Word Problems: Linear Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Writing equations

  1. 1. Solve:
    A\text{A}gym\text{gym}charges\text{charges}a\text{a}20\text{20}dollar\text{dollar}sign-up\text{sign-up}fee\text{fee}plus\text{plus}15\text{15}dollars\text{dollars}per\text{per}month.\text{month.}Write\text{Write}an\text{an}equation\text{equation}for\text{for}the\text{the}total\text{total}cost\text{cost}yy\text{}after\text{after}xx\text{}months.\text{months.}
  2. 2. Solve:
    A\text{A}plant\text{plant}is\text{is}4\text{4}cm\text{cm}tall\text{tall}and\text{and}grows\text{grows}2\text{2}cm\text{cm}per\text{per}week.\text{week.}Write\text{Write}an\text{an}equation\text{equation}for\text{for}its\text{its}height\text{height}yy\text{}after\text{after}xx\text{}weeks.\text{weeks.}
  3. 3. Solve:
    A\text{A}taxi\text{taxi}charges\text{charges}3\text{3}dollars\text{dollars}plus\text{plus}2\text{2}dollars\text{dollars}per\text{per}mile.\text{mile.}Write\text{Write}an\text{an}equation\text{equation}for\text{for}the\text{the}cost\text{cost}yy\text{}of\text{of}a\text{a}ride\text{ride}of\text{of}xx\text{}miles.\text{miles.}
  4. 4. Solve:
    Sam\text{Sam}has\text{has}50\text{50}dollars\text{dollars}and\text{and}spends\text{spends}5\text{5}dollars\text{dollars}each\text{each}day.\text{day.}Write\text{Write}an\text{an}equation\text{equation}for\text{for}the\text{the}money\text{money}yy\text{}left\text{left}after\text{after}xx\text{}days.\text{days.}
  5. 5. Solve:
    A\text{A}pool\text{pool}holds\text{holds}200\text{200}gallons\text{gallons}and\text{and}is\text{is}filled\text{filled}at\text{at}25\text{25}gallons\text{gallons}per\text{per}minute\text{minute}starting\text{starting}from\text{from}empty.\text{empty.}Write\text{Write}an\text{an}equation\text{equation}for\text{for}the\text{the}water\text{water}yy\text{}after\text{after}xx\text{}minutes.\text{minutes.}
  6. 6. Solve:
    A\text{A}phone\text{phone}plan\text{plan}costs\text{costs}30\text{30}dollars\text{dollars}per\text{per}month\text{month}plus\text{plus}10\text{10}dollars\text{dollars}per\text{per}GB\text{GB}of\text{of}data.\text{data.}Write\text{Write}an\text{an}equation\text{equation}for\text{for}the\text{the}monthly\text{monthly}cost\text{cost}yy\text{}for\text{for}xx\text{}GB.\text{GB.}
  7. 7. Solve:
    A\text{A}candle\text{candle}is\text{is}12\text{12}in\text{in}tall\text{tall}and\text{and}burns\text{burns}1\text{1}in\text{in}per\text{per}hour.\text{hour.}Write\text{Write}an\text{an}equation\text{equation}for\text{for}its\text{its}height\text{height}yy\text{}after\text{after}xx\text{}hours.\text{hours.}
  8. 8. Solve:
    A\text{A}worker\text{worker}earns\text{earns}18\text{18}dollars\text{dollars}per\text{per}hour\text{hour}plus\text{plus}a\text{a}40\text{40}dollar\text{dollar}bonus.\text{bonus.}Write\text{Write}an\text{an}equation\text{equation}for\text{for}the\text{the}pay\text{pay}yy\text{}for\text{for}xx\text{}hours.\text{hours.}

Answer Key

Level 1

  1. 1. y=15x+20y = 15x + 20
  2. 2. y=2x+4y = 2x + 4
  3. 3. y=2x+3y = 2x + 3
  4. 4. y=−5x+50y = -5x + 50
  5. 5. y=25xy = 25x
  6. 6. y=10x+30y = 10x + 30
  7. 7. y=−x+12y = -x + 12
  8. 8. y=18x+40y = 18x + 40

Grade 8 Algebra: Word Problems: Linear Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Using an equation

  1. 1. Solve:
    A\text{A}gym\text{gym}charges\text{charges}a\text{a}20\text{20}dollar\text{dollar}sign-up\text{sign-up}fee\text{fee}plus\text{plus}15\text{15}dollars\text{dollars}per\text{per}month.\text{month.}What\text{What}is\text{is}the\text{the}total\text{total}cost\text{cost}after\text{after}6\text{6}months?\text{months?}
  2. 2. Solve:
    A\text{A}plant\text{plant}is\text{is}4\text{4}cm\text{cm}tall\text{tall}and\text{and}grows\text{grows}2\text{2}cm\text{cm}per\text{per}week.\text{week.}After\text{After}how\text{how}many\text{many}weeks\text{weeks}will\text{will}it\text{it}be\text{be}18\text{18}cm\text{cm}tall?\text{tall?}
  3. 3. Solve:
    A\text{A}taxi\text{taxi}charges\text{charges}3\text{3}dollars\text{dollars}plus\text{plus}2\text{2}dollars\text{dollars}per\text{per}mile.\text{mile.}How\text{How}far\text{far}can\text{can}you\text{you}ride\text{ride}for\text{for}25\text{25}dollars?\text{dollars?}
  4. 4. Solve:
    A\text{A}tank\text{tank}has\text{has}80\text{80}liters\text{liters}and\text{and}drains\text{drains}4\text{4}liters\text{liters}per\text{per}minute.\text{minute.}When\text{When}will\text{will}it\text{it}be\text{be}empty?\text{empty?}
  5. 5. Solve:
    A\text{A}plumber\text{plumber}charges\text{charges}45\text{45}dollars\text{dollars}per\text{per}hour\text{hour}plus\text{plus}a\text{a}60\text{60}dollar\text{dollar}visit\text{visit}fee.\text{fee.}What\text{What}does\text{does}a\text{a}3\text{3}hour\text{hour}job\text{job}cost?\text{cost?}
  6. 6. Solve:
    A\text{A}car\text{car}has\text{has}12\text{12}gallons\text{gallons}of\text{of}gas\text{gas}and\text{and}uses\text{uses}0.5\text{0.5}gallons\text{gallons}per\text{per}hour\text{hour}of\text{of}driving.\text{driving.}How\text{How}much\text{much}gas\text{gas}is\text{is}left\text{left}after\text{after}8\text{8}hours?\text{hours?}
  7. 7. Solve:
    A\text{A}savings\text{savings}account\text{account}starts\text{starts}with\text{with}150\text{150}dollars\text{dollars}and\text{and}grows\text{grows}by\text{by}25\text{25}dollars\text{dollars}each\text{each}week.\text{week.}When\text{When}will\text{will}it\text{it}reach\text{reach}400\text{400}dollars?\text{dollars?}
  8. 8. Solve:
    A\text{A}printer\text{printer}has\text{has}500\text{500}sheets\text{sheets}and\text{and}prints\text{prints}20\text{20}pages\text{pages}per\text{per}minute.\text{minute.}How\text{How}many\text{many}sheets\text{sheets}are\text{are}left\text{left}after\text{after}12\text{12}minutes?\text{minutes?}

Answer Key

Level 2

  1. 1. $110\$110
  2. 2. 7 weeks7\text{ weeks}
  3. 3. 11 miles11\text{ miles}
  4. 4. 20 minutes20\text{ minutes}
  5. 5. $195\$195
  6. 6. 8 gallons8\text{ gallons}
  7. 7. 10 weeks10\text{ weeks}
  8. 8. 260 sheets260\text{ sheets}

Grade 8 Algebra: Word Problems: Linear Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Finding the equation from two facts

  1. 1. Solve:
    A\text{A}rental\text{rental}costs\text{costs}70\text{70}dollars\text{dollars}for\text{for}2\text{2}days\text{days}and\text{and}130\text{130}dollars\text{dollars}for\text{for}5\text{5}days.\text{days.}Write\text{Write}an\text{an}equation\text{equation}for\text{for}the\text{the}cost\text{cost}yy\text{}for\text{for}xx\text{}days.\text{days.}
  2. 2. Solve:
    A\text{A}plant\text{plant}was\text{was}9\text{9}cm\text{cm}tall\text{tall}after\text{after}2\text{2}weeks\text{weeks}and\text{and}15\text{15}cm\text{cm}tall\text{tall}after\text{after}5\text{5}weeks.\text{weeks.}Write\text{Write}an\text{an}equation\text{equation}for\text{for}its\text{its}height,\text{height,}and\text{and}give\text{give}its\text{its}starting\text{starting}height.\text{height.}
  3. 3. Solve:
    A\text{A}phone\text{phone}battery\text{battery}shows\text{shows}90\text{90}percent\text{percent}after\text{after}1\text{1}hour\text{hour}and\text{and}60\text{60}percent\text{percent}after\text{after}4\text{4}hours.\text{hours.}Write\text{Write}an\text{an}equation\text{equation}for\text{for}the\text{the}battery\text{battery}yy\text{}after\text{after}xx\text{}hours.\text{hours.}
  4. 4. Solve:
    A\text{A}caterer\text{caterer}charges\text{charges}230\text{230}dollars\text{dollars}for\text{for}10\text{10}guests\text{guests}and\text{and}390\text{390}dollars\text{dollars}for\text{for}18\text{18}guests.\text{guests.}What\text{What}is\text{is}the\text{the}cost\text{cost}per\text{per}guest\text{guest}and\text{and}the\text{the}fixed\text{fixed}fee?\text{fee?}
  5. 5. Solve:
    Plan\text{Plan}1\text{1}costs\text{costs}25\text{25}dollars\text{dollars}plus\text{plus}5\text{5}dollars\text{dollars}per\text{per}class.\text{class.}Plan\text{Plan}2\text{2}costs\text{costs}10\text{10}dollars\text{dollars}per\text{per}class.\text{class.}After\text{After}how\text{how}many\text{many}classes\text{classes}do\text{do}they\text{they}cost\text{cost}the\text{the}same?\text{same?}
  6. 6. Solve:
    A\text{A}hiker\text{hiker}is\text{is}2\text{2}miles\text{miles}from\text{from}camp\text{camp}after\text{after}1\text{1}hour\text{hour}and\text{and}8\text{8}miles\text{miles}from\text{from}camp\text{camp}after\text{after}4\text{4}hours,\text{hours,}walking\text{walking}away\text{away}at\text{at}a\text{a}steady\text{steady}pace.\text{pace.}How\text{How}far\text{far}will\text{will}the\text{the}hiker\text{hiker}be\text{be}after\text{after}6\text{6}hours?\text{hours?}
  7. 7. Solve:
    Water\text{Water}in\text{in}a\text{a}tank\text{tank}is\text{is}140\text{140}liters\text{liters}after\text{after}3\text{3}minutes\text{minutes}and\text{and}100\text{100}liters\text{liters}after\text{after}5\text{5}minutes\text{minutes}of\text{of}draining.\text{draining.}How\text{How}much\text{much}water\text{water}was\text{was}there\text{there}at\text{at}the\text{the}start?\text{start?}
  8. 8. Solve:
    A\text{A}store\text{store}charges\text{charges}4\text{4}dollars\text{dollars}per\text{per}notebook.\text{notebook.}Another\text{Another}charges\text{charges}2.5\text{2.5}dollars\text{dollars}per\text{per}notebook\text{notebook}plus\text{plus}a\text{a}6\text{6}dollar\text{dollar}fee.\text{fee.}For\text{For}how\text{how}many\text{many}notebooks\text{notebooks}are\text{are}the\text{the}costs\text{costs}equal?\text{equal?}

Answer Key

Level 3

  1. 1. y=20x+30y = 20x + 30
  2. 2. y=2x+5, 5 cmy = 2x + 5,\ 5\text{ cm}
  3. 3. y=−10x+100y = -10x + 100
  4. 4. $20 per guest, $30 fee\$20\text{ per guest},\ \$30\text{ fee}
  5. 5. 5 classes5\text{ classes}
  6. 6. 12 miles12\text{ miles}
  7. 7. 200 liters200\text{ liters}
  8. 8. 4 notebooks4\text{ notebooks}