To determine which given lines have the equation \( y = -5x + 4 \), we need to calculate the slope of each pair of points and see if it matches the slope of the given equation, which is -5.
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Line through (1, 9) and (3, 19): \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{19 - 9}{3 - 1} = \frac{10}{2} = 5 \] The slope is 5, which does not match -5.
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Line through (2, –14) and (4, –24): \[ \text{slope} = \frac{-24 - (-14)}{4 - 2} = \frac{-24 + 14}{2} = \frac{-10}{2} = -5 \] The slope is -5, which matches.
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Line through (1, 1) and (3, 11): \[ \text{slope} = \frac{11 - 1}{3 - 1} = \frac{10}{2} = 5 \] The slope is 5, which does not match -5.
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Line through (2, –6) and (4, –16): \[ \text{slope} = \frac{-16 - (-6)}{4 - 2} = \frac{-16 + 6}{2} = \frac{-10}{2} = -5 \] The slope is -5, which matches.
Therefore, the correct answers are the line passing through the points (2, –14) and (4, –24) and the line passing through the points (2, –6) and (4, –16). Both these lines have a slope of -5, which matches the given equation.
1 answer