Give a formula to find the x-intercept of the line y = mx + c.

Step-by-step solution

Idea: On the x-axis every point has y = 0. So set y = 0 and solve for x.

1. At the x-intercept the line meets the x-axis, where y = 0. So 0 = mx + c.1 mark
2. mx = −c ⇒ x = −cm, provided m ≠ 0. (If m = 0 the line y = c is horizontal: it has no x-intercept when c ≠ 0, and it is the x-axis itself when c = 0.)1 mark

Check: y = 2x − 6: formula gives −−62 = 3, and indeed 2(3) − 6 = 0 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Writing cm without the minus sign.
• Writing −mc (upside down).
• Forgetting that a horizontal line (m = 0) has no single x-intercept.

How this can come in the exam

Try one yourself

Find the x-intercept of y = −3x + 12.

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