Question

Which equation represents a line that is perpendicular to the line passing through (-4,7) and (1,3)?

Answer 1

The equation perpendicular to the line passing through the points (-4,7) and (1,3) is$y=\frac{5}{4}x-2$

Equation perpendicular to a line

The slope of the given line is calculated as:

$m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{3-7}{1-(-4)} \\\\m=\frac{-4}{5}$

The equation perpendicular to the given line will be of the form

$y-y_1=\frac{-1}{m} (x-x_1)$

Substitute $x_1=-4, y_1=7, and m=\frac{-4}{5}$

$y-7=\frac{5}{4}(x+4)\\\\ y=\frac{5}{4}x+5-7\\\\ y=\frac{5}{4}x-2$

Therefore, the equation perpendicular to the line passing through the points (-4,7) and (1,3) is $y=\frac{5}{4}x-2$

Learn more on perpendicular equations here: brainly.com/question/1441594

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