1. **State the problem:** We need to find the gradient (slope) and the y-intercept of the line passing through the points (0, 10) and (10, 40). 2. **Formula for gradient:** The gradient $m$ of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the gradient:** Using the points $(0, 10)$ and $(10, 40)$: $$m = \frac{40 - 10}{10 - 0} = \frac{30}{10} = 3$$ 4. **Find the y-intercept:** The y-intercept is the value of $y$ when $x=0$. From the point $(0, 10)$, the y-intercept is clearly $10$. 5. **Equation of the line:** Using the slope-intercept form $y = mx + c$, where $m$ is the gradient and $c$ is the y-intercept, we have: $$y = 3x + 10$$ **Final answer:** - Gradient (slope) $m = 3$ - Y-intercept $c = 10$