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Linear Equations Practice

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Linear Equations Practice

Choose one answer for each multiple-choice question. Show your working for written questions. Use y = mx + c when writing an equation in gradient-intercept form.

Multiple Choice

1.A line has gradient 2 and passes through (3, 8). Which equation describes it?

y = 2x + 2
y = 2x + 5
y = 3x + 2
y = 2x − 8

2.Which equation has a gradient of −3?

y = 3x − 4
y = −3x + 4
y = −x − 3
y = 4x − 3

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

4.Which set contains only equations that can describe straight lines?

y = 4x − 1; 2x + y = 7; y − 3 = 2(x + 1)
y = x²; y = 4x − 1; 2x + y = 7
y = 1/x; y = 4x − 1; y − 3 = 2(x + 1)
y = x²; y = 1/x; 2x + y = 7

Match the Line Information

Match each line description to its equation. Use each equation once.

5.Match each description with the correct equation.

Gradient 3, y-intercept 2
Gradient −1, y-intercept 5
Passes through (0, −4) and (2, 0)
Gradient 1, passes through (1, −2)

y = 3x + 2
y = x − 3
y = −x + 5
y = 2x − 4

Find the Equation

Write each answer in the form y = mx + c. Include working.

6.Find the equation of the line with gradient 5 that passes through (2, 1).

7.Find the equation of the line through (0, 4) and (3, 10).

8.A line has gradient −2 and passes through (1, 6). Find its equation.

9.Find the equation of the line through (−2, 3) and (2, −5).

Use Linear Equations

10.A bike hire service charges a fixed fee of $8 plus $6 for each hour hired. Write an equation for the total cost C dollars for h hours.

11.A water tank contains 30 litres at the start of a test. Water flows in at 4 litres per minute. Write an equation for the volume V after t minutes, then calculate the volume after 7 minutes.