Success TutoringWorksheets

Year 8 Gradient and Linear Equations Worksheet — Level 1 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 8 linear relationships & graphs worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Linear Relationships & Graphs

Year 8 Gradient and Linear Equations Worksheet — Level 1 — Practice Set 3 — Answers

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

1.Find the gradient of the line through (−4, 1) and (−8, −11).

Answer: 3

  1. gradient = rise ÷ run = (−11 − 1) ÷ (−8 − (−4))
  2. = −12 ÷ −4 = 3
2.Find the gradient of the line through (2, −5) and (−3, −15).

Answer: 2

  1. gradient = rise ÷ run = (−15 − (−5)) ÷ (−3 − 2)
  2. = −10 ÷ −5 = 2
3.Find the gradient of the line through (5, 2) and (4, −1).

Answer: 3

  1. gradient = rise ÷ run = (−1 − 2) ÷ (4 − 5)
  2. = −3 ÷ −1 = 3
4.Find the gradient of the line through (6, 4) and (5, 6).

Answer: −2

  1. gradient = rise ÷ run = (6 − 4) ÷ (5 − 6)
  2. = 2 ÷ −1 = −2
5.Find the gradient of the line through (2, −3) and (7, 7).

Answer: 2

  1. gradient = rise ÷ run = (7 − (−3)) ÷ (7 − 2)
  2. = 10 ÷ 5 = 2
6.Find the gradient of the line through (−3, −2) and (−4, −4).

Answer: 2

  1. gradient = rise ÷ run = (−4 − (−2)) ÷ (−4 − (−3))
  2. = −2 ÷ −1 = 2
7.For the line y = −3x + 5, write the gradient and the y-intercept.

Answer: gradient −3; y-intercept 5

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

8.For the line y = −x + 7, write the gradient and the y-intercept.

Answer: gradient −1; y-intercept 7

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

9.For the line y = −4x − 7, write the gradient and the y-intercept.

Answer: gradient −4; y-intercept −7

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

10.Find the gradient of the line through (−4, 3) and (−5, 6).

Answer: −3

  1. gradient = rise ÷ run = (6 − 3) ÷ (−5 − (−4))
  2. = 3 ÷ −1 = −3
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Marking tips

  • Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
  • For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
  • Celebrate what went well first, then pick one thing to work on next.

Great work. Here's what to try next: