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Finding Line Equations Worksheet

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Finding Line Equations Worksheet

Use the form y = mx + c, where m is the gradient and c is the y-intercept. Show your working for calculation questions.

Read a line from its features

For a line in the form y = mx + c, the gradient is m and the y-intercept is c.

1.A line passes through (0, 2) and (3, 11). State its y-intercept and gradient, then write its equation in the form y = mx + c.

2.A line has gradient −2 and crosses the y-axis at 5. Which equation represents the line?

y = −2x + 5
y = 5x − 2
y = 2x + 5
y = −2x − 5

3.Match each equation with its gradient and y-intercept.

y = 4x − 3
y = −x + 6
y = 0.25x + 2

Gradient −1; y-intercept 6
Gradient 0.25; y-intercept 2
Gradient 4; y-intercept −3

Find an equation from two points

Calculate the gradient using the change in y divided by the change in x. Then substitute one point into y = mx + c to find c.

4.Find the equation of the line through (1, 4) and (4, 13). Show how you calculate the gradient and y-intercept.

5.Find the equation of the line passing through (−2, 7) and (2, −1).

6.Which equation describes the line through (0, −3) and (3, 6)?

y = 3x − 3
y = −3x − 3
y = 3x + 3
y = x − 3

Apply line equations

Use a linear equation to model each situation. Include units where appropriate.

7.A bike hire shop charges a fixed fee of $12 plus $4 per hour. Let x be the number of hours and y the total cost in dollars. Write an equation for the cost, then calculate the cost for 5 hours.

8.A parallel line to y = 2x + 4 passes through (3, 1). Find its equation in the form y = mx + c.

9.A water tank starts with 420 litres and loses 30 litres each minute. Write an equation for the water remaining y litres after x minutes, then find how much remains after 9 minutes.