Standard form of a linear equation · 1 mark

Write a linear equation in two variables in which a = 3, b = 0 and c = −15.

Answer: 3x + 0×y − 15 = 0, that is, 3x − 15 = 0 (or 15x − 1 = 0).

Step-by-step solution

Idea: Put the given values straight into the standard form ax + by + c = 0. Because b = 0, the y-term is 0×y; the equation is still treated as an equation in two variables.

Standard form: ax + by + c = 0. Substitute a = 3, b = 0, c = −15: 3x + 0×y − 15 = 0.½ mark
This is 3x − 15 = 0. Multiplying by 5 to clear the fraction gives the neater form 15x − 1 = 0 (in that form the values are 15, 0, −1, so give the first form when the exact a, b, c are asked for).½ mark

3x + 0·y − 1/5 = 0, i.e. 3x − 1/5 = 0.

Check: Any pair with x = 115 works, whatever y is: 3 × 115 − 15 = 15 − 15 = 0 ✓.

Answer to write in the exam

ax + by + c = 0 with a = 3, b = 0, c = −15

∴ 3x + 0×y − 15 = 0, i.e. 3x − 15 = 0

Common mistakes that cost marks

Writing 3x − 15y = 0, putting c in place of b.
Writing 3x + 15 = 0: c is negative, so the constant term is −15.
Thinking an equation with b = 0 is not allowed. Only a and b both being zero is ruled out.

How this can come in the exam

MCQ (1 mark)

Which equation has a = 0, b = 2 and c = 7 in the form ax + by + c = 0?

2x + 7 = 0
2y + 7 = 0
2y = 7
7y + 2 = 0

Show answer

(B) 2y + 7 = 0
0×x + 2y + 7 = 0 is 2y + 7 = 0.

Try one yourself

Write a linear equation in two variables with a = −2, b = 5 and c = 0.