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Gradient and Coordinates Worksheet

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Gradient and Coordinates Worksheet

Show your working and simplify fractions where possible. Use m = (y₂ − y₁) ÷ (x₂ − x₁). For a line written as y = mx + c, m is the gradient and c is the y-intercept.

Foundation skills

Calculate gradients, classify lines and read linear equations.

1.Find the gradient of the line through (2, 1) and (6, 9).

2.Calculate the gradient of the line joining U(0, −2) and V(5, 8).

3.Match each line equation to its gradient classification: y = 4; x = −2; y = 3x − 1; y = −2x + 5.

y = 4
x = −2
y = 3x − 1
y = −2x + 5

Positive gradient
Horizontal: gradient 0
Vertical: gradient undefined
Negative gradient

4.For the equation y = 4x + 7, state the gradient and y-intercept.

5.For the equation y = −2x − 3, state the gradient and y-intercept.

Application and problem solving

Use gradients to solve coordinate and equation problems.

6.Find the gradient of the line through A(−3, 5) and B(2, −5). Give your answer in simplest form.

7.A line passes through (2, 1) and (6, k), and its gradient is 3. Find k.

8.Determine whether the line through L(−2, 0) and M(2, 8) is parallel to the line through N(1, −3) and P(4, 3). Show how you compare their gradients.

9.Rearrange 4x + 3y = 18 into y = mx + c form, then state the gradient.

10.The gradient of the line through (p, 9) and (5, 3) is −2. Find p.

Reasoning and extension

Explain your reasoning and use gradient relationships to investigate lines and shapes.

11.A student finds the gradient between C(−3, 7) and D(3, −2) using (−3 − 7) ÷ (3 − (−2)). Identify the error and calculate the correct gradient.

12.Points A(2, 1), B(5, 7) and C(8, k) lie on one straight line. Find k by equating the gradients AB and BC.

13.The vertices of quadrilateral WXYZ are W(1, 1), X(7, 3), Y(9, 9) and Z(3, 7). Find the gradient of each side in order and classify the quadrilateral. Justify your classification using the gradients.

14.Line 1 passes through (2, 4) and (6, 12). Line 2 passes through (1, 5) and (5, t). Find t so that the lines are perpendicular. Use the fact that perpendicular gradients multiply to −1.