Subjects algebra

Calculate Gradient

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1. The problem is to find the gradient (slope) between two points using the formula $$m=\frac{y_2 - y_1}{x_2 - x_1}$$. 2. For points (5, 4) and (7, 0): $$m=\frac{0 - 4}{7 - 5}=\frac{-4}{2}=-2$$ 3. For points (-3, 4) and (4, 8): $$m=\frac{8 - 4}{4 - (-3)}=\frac{4}{7}$$ 4. For points (3, 7) and (1, 10): $$m=\frac{10 - 7}{1 - 3}=\frac{3}{-2}=-\frac{3}{2}$$ 5. For points (8, 1) and (3, -3): $$m=\frac{-3 - 1}{3 - 8}=\frac{-4}{-5}=\frac{4}{5}$$ 6. For points (3, -1) and (-2, 9): $$m=\frac{9 - (-1)}{-2 - 3}=\frac{10}{-5}=-2$$ 7. For Graph 1, points (2, 0) and (0, -3): $$m=\frac{-3 - 0}{0 - 2}=\frac{-3}{-2}=\frac{3}{2}$$ 8. For Graph 2, points (-3, 0) and (0, -6): $$m=\frac{-6 - 0}{0 - (-3)}=\frac{-6}{3}=-2$$ Final answers: 1. -2 2. \frac{4}{7} 3. -\frac{3}{2} 4. \frac{4}{5} 5. -2 6. \frac{3}{2} 7. -2