Year 10 Gradient and Linear Equations Worksheet — Level 3 — Answers

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

Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Linear Relationships & Graphs

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 + 4, write the gradient and the y-intercept.

Answer: gradient −1; y-intercept 4

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.Does the point (−1, −5) lie on the line y = 5x + 3?

Answer: No

Substitute x = −1: y = 5 × (−1) + 3 = −2, not −5.

3.Does the point (−4, −13) lie on the line y = 3x + 2?

Answer: No

Substitute x = −4: y = 3 × (−4) + 2 = −10, not −13.

4.For the line y = −5x, write the gradient and the y-intercept.

Answer: gradient −5; 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.

5.Does the point (0, −1) lie on the line y = −x − 1?

Answer: Yes

Substitute x = 0: y = −1 × 0 − 1 = −1, which matches.

6.Does the point (2, −8) lie on the line y = −4x?

Answer: Yes

Substitute x = 2: y = −4 × 2 + 0 = −8, which matches.

7.Does the point (4, 2) lie on the line y = 3x − 9?

Answer: No

Substitute x = 4: y = 3 × 4 − 9 = 3, not 2.

8.For the line y = x + 4, write the gradient and the y-intercept.

Answer: gradient 1; y-intercept 4

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.Does the point (−5, 22) lie on the line y = −4x + 5?

Answer: No

Substitute x = −5: y = −4 × (−5) + 5 = 25, not 22.

10.Does the point (5, 12) lie on the line y = x + 9?

Answer: No

Substitute x = 5: y = 1 × 5 + 9 = 14, not 12.

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