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]
