The equation perpendicular to the line passing through the points (-4,7) and (1,3) is[tex]y=\frac{5}{4}x-2[/tex]
Equation perpendicular to a line
The slope of the given line is calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{3-7}{1-(-4)} \\\\m=\frac{-4}{5}[/tex]
The equation perpendicular to the given line will be of the form
[tex]y-y_1=\frac{-1}{m} (x-x_1)[/tex]
Substitute [tex]x_1=-4, y_1=7, and m=\frac{-4}{5}[/tex]
[tex]y-7=\frac{5}{4}(x+4)\\\\ y=\frac{5}{4}x+5-7\\\\ y=\frac{5}{4}x-2[/tex]
Therefore, the equation perpendicular to the line passing through the points (-4,7) and (1,3) is [tex]y=\frac{5}{4}x-2[/tex]
Learn more on perpendicular equations here: https://brainly.com/question/1441594
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