Answer:
[tex]y-3=-\frac{3}{8} (x+2)[/tex]
Step-by-step explanation:
We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have a point (8,1) and a slope from the equation. We will chose point-slope since we have a point and slope.
Point slope:[tex]y-y_1=m(x-x_1)[/tex]
[tex]m\neq \frac{8}{3}[/tex] in our new equation because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is [tex]m=-\frac{3}{8}[/tex].
We will substitute [tex]m=-\frac{3}{8}[/tex] and [tex]x_1=-2\\y_1=3[/tex].
[tex]y-3=-\frac{3}{8} (x-(-2))[/tex]
[tex]y-3=-\frac{3}{8} (x+2)[/tex]
This is the equation of the line perpendicular to the equation given that crosses through (-2,3).
