Slope and rate of change

Slope, the rate of change read off a table, and comparing two rates — three ways of asking how fast something changes.

5 sheets · 30 questions · one answer key · 6 pages

Recommended for grades 8–9

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Slope from a graph Sheet 1 of 5

Slope and y-interceptSlope from an equation

Name: Date:

Write the slope of each line.

1y = −9x + 17m =

2y = 11xm =

3y = −6x − 19m =

4y = −21m =

5y = x − 6m =

6y = 10x + 30m =

Slope and y-interceptThe y-intercept

Name: Date:

Write the y-intercept of each line.

1y = −6x − 16b =

2y = 4x − 28b =

3y = −12xb =

4y = −8x − 26b =

5y = 3x + 29b =

6y = 9x + 34b =

Slope and y-interceptSlope from two points

Name: Date:

Find the slope of the line through each pair of points.

1(−3, −4) and (1, 16)m =

2(2, 6) and (3, 10)m =

3(−1, −4) and (4, −29)m =

4(4, 1) and (7, 1)m =

5(−4, 3) and (0, 3)m =

6(−3, 2) and (1, −2)m =

Rate of changeThe rate of change

Name: Date:

Each table is a straight line. Find what each one asks for.

1x3456y181260rate

2x2345y58494031rate

3x7121722y56463626rate

4x6121824y32445668rate

5x9111315y66768696rate

6x78910y27231915rate

Which rate is greaterAn equation against a written rate

Name: Date:

Which one is greater, A or B? Work out each rate first. Circle one.

1A36 meters in 4 secondsBy = 15x, y meters and x secondsAB

2Ay = 4x, y dollars and x weeksB30 dollars in 5 weeksAB

3Ay = 15x, y dollars and x weeksB18 dollars in 9 weeksAB

4A135 liters in 9 minutesBy = 12x, y liters and x minutesAB

5Ay = 13x, y pages and x daysB18 pages in 2 daysAB

6A20 km in 4 hoursBy = 6x, y km and x hoursAB

Power Pack · Slope and rate of changeAnswer key

Slope from a graph

1. y = −9x + 17 → m = −92. y = 11x → m = 113. y = −6x − 19 → m = −64. y = −21 → m = 05. y = x − 6 → m = 16. y = 10x + 30 → m = 10

Reading the intercept

1. y = −6x − 16 → b = −162. y = 4x − 28 → b = −283. y = −12x → b = 04. y = −8x − 26 → b = −265. y = 3x + 29 → b = 296. y = 9x + 34 → b = 34

Slope from two points

1. (−3, −4) and (1, 16) → m = 52. (2, 6) and (3, 10) → m = 43. (−1, −4) and (4, −29) → m = −54. (4, 1) and (7, 1) → m = 05. (−4, 3) and (0, 3) → m = 06. (−3, 2) and (1, −2) → m = −1

Rate from a table

1. x: 3, 4, 5, 6 y: 18, 12, 6, 0 → −6 (y moves −6 while x moves 1, and −6 ÷ 1 = −6)2. x: 2, 3, 4, 5 y: 58, 49, 40, 31 → −9 (y moves −9 while x moves 1, and −9 ÷ 1 = −9)3. x: 7, 12, 17, 22 y: 56, 46, 36, 26 → −2 (y moves −10 while x moves 5, and −10 ÷ 5 = −2)4. x: 6, 12, 18, 24 y: 32, 44, 56, 68 → 2 (y moves 12 while x moves 6, and 12 ÷ 6 = 2)5. x: 9, 11, 13, 15 y: 66, 76, 86, 96 → 5 (y moves 10 while x moves 2, and 10 ÷ 2 = 5)6. x: 7, 8, 9, 10 y: 27, 23, 19, 15 → −4 (y moves −4 while x moves 1, and −4 ÷ 1 = −4)

Compare rates

1. A 36 meters in 4 seconds B y = 15x, y meters and x seconds → B (A is 9 and B is 15 per second)2. A y = 4x, y dollars and x weeks B 30 dollars in 5 weeks → B (A is 4 and B is 6 per week)3. A y = 15x, y dollars and x weeks B 18 dollars in 9 weeks → A (A is 15 and B is 2 per week)4. A 135 liters in 9 minutes B y = 12x, y liters and x minutes → A (A is 15 and B is 12 per minute)5. A y = 13x, y pages and x days B 18 pages in 2 days → A (A is 13 and B is 9 per day)6. A 20 km in 4 hours B y = 6x, y km and x hours → B (A is 5 and B is 6 per hour)

Slope and rate of change

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