iGCSE Mathematics (0580) - C3.3 Gradient of linear graphs- Exam Style Questions Paper 1- New Syllabus
▶️ Answer/Explanation
(a) First, find where the line crosses the $y$-axis; it intersects at $(0, 3)$, so $c = 3$. Next, determine the gradient ($m$) by finding the rise over run between two points, such as $(0, 3)$ and $(2, 4)$, which gives $m = \frac{4 – 3}{2 – 0} = \frac{1}{2}$. Thus, the equation is $y = \frac{1}{2}x + 3$.
(b) Where the line hits the $x$-axis, the value of $y$ must be 0. Substituting $y = 0$ into our equation gives $0 = \frac{1}{2}x + 3$, which simplifies to $\frac{1}{2}x = -3$, meaning $x = -6$. So, the coordinates are $(-6, 0)$.
✅ Answer:
(a) $y = \frac{1}{2}x + 3$
(b) (-6, 0)
(b) Where the line hits the $x$-axis, the value of $y$ must be 0. Substituting $y = 0$ into our equation gives $0 = \frac{1}{2}x + 3$, which simplifies to $\frac{1}{2}x = -3$, meaning $x = -6$. So, the coordinates are $(-6, 0)$.
✅ Answer:
(a) $y = \frac{1}{2}x + 3$
(b) (-6, 0)
