iGCSE Mathematics (0580) - C3.6 Parallel lines- Exam Style Questions Paper 1- New Syllabus

(a) Both linear equations are written in the standard form $y = mx + c$, where $m$ is the gradient. For line A, the gradient is 3, and for line B, the gradient is also 3. Since they have identical gradients but different y-intercepts ($+1$ and $-1$), the lines run in exactly the same direction and will never meet. Thus, Line A is parallel to line B.

(b) To plot $y = 2x – 1$, we can find a couple of coordinates:
• If $x = 0$, $y = 2(0) – 1 = -1 \rightarrow (0, -1)$
• If $x = 1$, $y = 2(1) – 1 = 1 \rightarrow (1, 1)$
• If $x = 2$, $y = 2(2) – 1 = 3 \rightarrow (2, 3)$ Plot these points on the provided coordinate grid and draw a single straight line through them using a ruler.

Answers:
(a) Ring around: Line A is parallel to line B
(b) [A straight line passing through $(0, -1)$, $(1, 1)$, and $(2, 3)$]