QuestionAugust 25, 2025

6) through: (5,1) perp.to y=-(5)/(2)x+4

6) through: (5,1) perp.to y=-(5)/(2)x+4
6) through: (5,1) perp.to y=-(5)/(2)x+4

Solution
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Answer

y = \frac{2}{5}x - 1 Explanation 1. Identify the slope of the given line The slope of the line y = -\frac{5}{2}x + 4 is -\frac{5}{2}. 2. Determine the perpendicular slope The slope of a line perpendicular to another is the negative reciprocal. So, the perpendicular slope is \frac{2}{5}. 3. Use point-slope form to find the equation Use the point (5, 1) and the slope \frac{2}{5} in the point-slope formula: y - y_1 = m(x - x_1). Substitute: y - 1 = \frac{2}{5}(x - 5). 4. Simplify the equation Distribute and simplify: y - 1 = \frac{2}{5}x - 2. Add 1 to both sides: y = \frac{2}{5}x - 1.

Explanation

1. Identify the slope of the given line<br /> The slope of the line $y = -\frac{5}{2}x + 4$ is $-\frac{5}{2}$.<br /><br />2. Determine the perpendicular slope<br /> The slope of a line perpendicular to another is the negative reciprocal. So, the perpendicular slope is $\frac{2}{5}$.<br /><br />3. Use point-slope form to find the equation<br /> Use the point $(5, 1)$ and the slope $\frac{2}{5}$ in the point-slope formula: $y - y_1 = m(x - x_1)$.<br /> Substitute: $y - 1 = \frac{2}{5}(x - 5)$.<br /><br />4. Simplify the equation<br /> Distribute and simplify: $y - 1 = \frac{2}{5}x - 2$.<br /> Add 1 to both sides: $y = \frac{2}{5}x - 1$.
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