Success TutoringWorksheets

Year 10 Gradient and Linear Equations Worksheet — Level 2 — Practice Set 3 — Answers

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

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Linear Relationships & Graphs

Year 10 Gradient and Linear Equations Worksheet — Level 2 — 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.For the line y = −x + 5, write the gradient and the y-intercept.

Answer: gradient −1; 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.

2.For the line y = x − 1, write the gradient and the y-intercept.

Answer: gradient 1; y-intercept −1

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

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

Answer: y = 2x − 4

  1. y = 2x + (y-intercept)
  2. −10 = 2 × (−3) + (y-intercept)
  3. y-intercept = −10 − (−6) = −4
  4. y = 2x − 4
4.Find the gradient of the line through (−3, 4) and (−1, 3).

Answer: −

  1. gradient = rise ÷ run = (3 − 4) ÷ (−1 − (−3))
  2. = −1 ÷ 2 = −
5.A line has a gradient of −1 and passes through (4, 2). Find its equation.

Answer: y = −x + 6

  1. y = −1x + (y-intercept)
  2. 2 = −1 × 4 + (y-intercept)
  3. y-intercept = 2 − (−4) = 6
  4. y = −x + 6
6.For the line y = 6x + 7, write the gradient and the y-intercept.

Answer: gradient 6; 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.

7.For the line y = 2x + 3, write the gradient and the y-intercept.

Answer: gradient 2; y-intercept 3

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.Find the gradient of the line through (−3, 4) and (−2, 3).

Answer: −1

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

Answer: gradient 4; y-intercept 0

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 (3, −6).

Answer: 3

  1. gradient = rise ÷ run = (−6 − (−3)) ÷ (3 − 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: