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10th Grade Slope and Linear Equations Worksheet — Level 3 — Practice Set 4 — Answers

Answer sheet with worked solutions for the 10th Grade linear relationships & graphs worksheet.

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10th Grade Slope and Linear Equations Worksheet — Level 3 — Practice Set 4 — Answers

Show your work. Slope = rise ÷ run; the equation of a line can be written as y = (slope)x + (y-intercept).

1.Does the point (−5, 24) lie on the line y = −3x + 7?
  1. AYes
  2. BNo

Answer: No

Substitute x = −5: y = −3 × (−5) + 7 = 22, not 24.

2.A line has a slope of 5 and passes through (−1, 2). Find its equation.

Answer: y = 5x + 7

  1. y = 5x + (y-intercept)
  2. 2 = 5 × (−1) + (y-intercept)
  3. y-intercept = 2 − (−5) = 7
  4. y = 5x + 7
3.Does the point (−4, 5) lie on the line y = −2x?
  1. AYes
  2. BNo

Answer: No

Substitute x = −4: y = −2 × (−4) + 0 = 8, not 5.

4.A line has a slope of 5 and passes through (3, 24). Find its equation.

Answer: y = 5x + 9

  1. y = 5x + (y-intercept)
  2. 24 = 5 × 3 + (y-intercept)
  3. y-intercept = 24 − 15 = 9
  4. y = 5x + 9
5.Does the point (−5, 19) lie on the line y = −4x?
  1. AYes
  2. BNo

Answer: No

Substitute x = −5: y = −4 × (−5) + 0 = 20, not 19.

6.For the line y = x − 2, write the slope and the y-intercept.

Answer: slope 1; y-intercept −2

In y = (slope)x + (y-intercept), the number multiplying x is the slope and the constant is where the line crosses the y-axis.

7.A line has a slope of 1 and passes through (4, 13). Find its equation.

Answer: y = x + 9

  1. y = 1x + (y-intercept)
  2. 13 = 1 × 4 + (y-intercept)
  3. y-intercept = 13 − 4 = 9
  4. y = x + 9
8.Does the point (3, −10) lie on the line y = −x − 7?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = 3: y = −1 × 3 − 7 = −10, which matches.

9.For the line y = x − 6, write the slope and the y-intercept.

Answer: slope 1; y-intercept −6

In y = (slope)x + (y-intercept), the number multiplying x is the slope and the constant is where the line crosses the y-axis.

10.A line has a slope of −1 and passes through (−3, −2). Find its equation.

Answer: y = −x − 5

  1. y = −1x + (y-intercept)
  2. −2 = −1 × (−3) + (y-intercept)
  3. y-intercept = −2 − 3 = −5
  4. y = −x − 5
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