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A line contains the points (–2, –6) and (4, 1). Using point-slope form, write the equation of the line that is perpendicular to the given line and that passes through the point (4, 1).

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MrsStrong

Answer:

[tex]y-1=-\frac{6}{7}(x-4)[/tex]

Step-by-step explanation:

Using the slope formula, substitute the points (-2,-6) and (4,1).

[tex]m=\frac{y_2-y_1}{x_2-x_1}  = \frac{1--6}{4--2} =\frac{7}{6}[/tex]

This is the slope of the two points. The slope perpendicular to it will be the negative reciprocal -6/7. Substitute m = -6/7 and the point (4,1) into the point to write the equation of the line.

[tex]y-y_1 = m(x-x_1)\\y-1=-\frac{6}{7}(x-4)[/tex]