Subjects algebra

Line Gradient 95320A

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1. **State the problem:** Find the gradient of the line passing through points (0, 7) and (4, 0). 2. **Formula:** The gradient (slope) $m$ of a line 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. **Apply the formula:** Using points $(0, 7)$ and $(4, 0)$: $$m = \frac{0 - 7}{4 - 0} = \frac{-7}{4}$$ 4. **Simplify:** $$m = -1.75$$ 5. **Interpretation:** The gradient is approximately $-1.75$, which lies between the options $-2$ and $-1$. The closest exact value is $-1.75$. **Final answer:** The gradient of the line is approximately $-1.75$.