Linear functions and slope test

Slope, intercepts, and rate of change — the same line described from three directions.

Linear functions and slope test

The answer key prints on a separate page.

What's on this test

Slope is rise over run, and the reliable error is the fraction upside down: run over rise reads the steepness backward and gets worse the steeper the line. Section 1 isolates it before the intercepts arrive, because the intercepts are where a second confusion waits — the y-intercept is the value when x is zero, read off the vertical axis, and it is routinely taken from the wrong one.

How the paper is put together

The equation of a line and rate of change are put last on purpose: they are the previous two sections said in words. y = mx + b is nothing but the slope and the intercept given names, and rate of change is slope with a unit attached — dollars per hour, miles per gallon. A child who can find a slope but not a rate of change has not met a new skill; they have met the same one wearing a story.

Math test

Name: Date:

1. Slope and y-interceptWrite the slope of each line.6 questions

1y = −2x − 22m =

2y = 2x − 5m =

3y = −2x − 27m =

4y = −12x − 15m =

5y = −12x − 3m =

6y = −4x − 6m =

2. Intercepts of a lineFind the x-intercept of each line.5 questions

79x − 2y = 18the x-intercept =

8x + y = −6the x-intercept =

94x − y = 8the x-intercept =

10x − 3y = −6the x-intercept =

112x − y = −4the x-intercept =

3. Write the equation of a lineWrite the equation of each line through the two points.5 questions

12through (2, 0) and (4, 2)y =x

13through (−3, 3) and (−1, −1)y =x

14through (1, 6) and (3, 10)y =x

15through (2, −13) and (4, −17)y =x

16through (−3, −12) and (−1, −6)y =x

Math test

4. Rate of change from a tableEach table is a straight line. Find what each one asks for.5 questions

17x2345y58494031rate

18x271217y5101520rate

19x3456y33404754rate

20x7111519y39475563rate

21x891011y26232017rate

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Answer key

Slope and y-intercept

1. y = −2x − 22 → m = −22. y = 2x − 5 → m = 23. y = −2x − 27 → m = −24. y = −12x − 15 → m = −125. y = −12x − 3 → m = −126. y = −4x − 6 → m = −4

Intercepts of a line

7. 9x − 2y = 18 the x-intercept = 28. x + y = −6 the x-intercept = −69. 4x − y = 8 the x-intercept = 210. x − 3y = −6 the x-intercept = −611. 2x − y = −4 the x-intercept = −2

Write the equation of a line

12. through (2, 0) and (4, 2) → y = x − 213. through (−3, 3) and (−1, −1) → y = −2x − 314. through (1, 6) and (3, 10) → y = 2x + 415. through (2, −13) and (4, −17) → y = −2x − 916. through (−3, −12) and (−1, −6) → y = 3x − 3

Rate of change from a table

17. x: 2, 3, 4, 5 y: 58, 49, 40, 31 → −9 (y moves −9 while x moves 1, and −9 ÷ 1 = −9)18. x: 2, 7, 12, 17 y: 5, 10, 15, 20 → 1 (y moves 5 while x moves 5, and 5 ÷ 5 = 1)19. x: 3, 4, 5, 6 y: 33, 40, 47, 54 → 7 (y moves 7 while x moves 1, and 7 ÷ 1 = 7)20. x: 7, 11, 15, 19 y: 39, 47, 55, 63 → 2 (y moves 8 while x moves 4, and 8 ÷ 4 = 2)21. x: 8, 9, 10, 11 y: 26, 23, 20, 17 → −3 (y moves −3 while x moves 1, and −3 ÷ 1 = −3)

Linear functions and slope test

What's on this test

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