1. **Problem Statement:** Find the gradient (slope) and y-intercept of the lines given by the graphs (a) and (b). 2. **Formula for slope (gradient):** $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line. 3. **Y-intercept:** The y-value when $x=0$. --- ### (a) Line passing through points $(0,10)$ and $(60,40)$: 4. Calculate the slope: $$m = \frac{40 - 10}{60 - 0} = \frac{30}{60}$$ 5. Simplify the fraction: $$m = \frac{\cancel{30}}{\cancel{60}} = \frac{1}{2}$$ 6. The y-intercept is the y-value when $x=0$, which is $10$. **Answer for (a):** - Gradient (slope) $m = \frac{1}{2}$ - Y-intercept $= 10$ --- ### (b) Line passing through points $(0,10)$ and $(6,0)$: 7. Calculate the slope: $$m = \frac{0 - 10}{6 - 0} = \frac{-10}{6}$$ 8. Simplify the fraction: $$m = \frac{\cancel{-10}}{\cancel{6}} = -\frac{5}{3}$$ 9. The y-intercept is the y-value when $x=0$, which is $10$. **Answer for (b):** - Gradient (slope) $m = -\frac{5}{3}$ - Y-intercept $= 10$