iGCSE Mathematics (0580) - C3.5 Equations of linear graphs- Exam Style Questions Paper 3- New Syllabus
▶️ Answer/Explanation
Find the y-intercept ($c$): The line crosses the y-axis at $y = 5$, so $c = 5$.
Find the gradient ($m$): Using points $(0, 5)$ and $(1, 8)$, $m = \frac{\text{change in } y}{\text{change in } x} = \frac{8 – 5}{1 – 0} = \frac{3}{1} = 3$.
Substitute $m$ and $c$ into $y = mx + c$:
✅ Answer: $y = 3x + 5$
▶️ Answer/Explanation
(a)
First, identify the y-intercept ($c$) from the graph, which is at $y = 2$. Next, calculate the gradient ($m$) by finding the ‘rise over run’ between two clear points like $(0,2)$ and $(4,3)$.
$m = \frac{3 – 2}{4 – 0} = \frac{1}{4}$
The equation is $y = \frac{1}{4}x + 2$.
✅ Answer: $y = \frac{1}{4}x + 2$
(b)
Parallel lines share the exact same gradient, so our new line has $m = -3$.
We substitute the known point $(1, 5)$ into the formula $y = -3x + c$ to find the new intercept.
$5 = -3(1) + c$
$c = 8$
So the full equation is $y = -3x + 8$.
✅ Answer: $y = -3x + 8$