Subjects algebra

Line Gradient Yintercept 1A9331

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1. **State the problem:** We need to find the gradient (slope) and the y-intercept of the line shown on the graph. 2. **Identify points on the line:** From the description, the line passes through approximately the points $(0, 20)$ and $(15, 60)$. 3. **Formula for gradient:** The gradient $m$ of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 4. **Calculate the gradient:** Substitute the points: $$m = \frac{60 - 20}{15 - 0} = \frac{40}{15}$$ 5. **Simplify the fraction:** $$m = \frac{\cancel{40}}{\cancel{15}} = \frac{8}{3}$$ 6. **Find the y-intercept:** The y-intercept is the value of $y$ when $x=0$. From the point $(0, 20)$, the y-intercept is $20$. 7. **Final answer:** - Gradient (slope) $m = \frac{8}{3}$ - Y-intercept $= 20$