Answer:
[tex]y-8=-\frac{7}{3} (x-14)[/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 and a slope from the equation. We will chose point-slope since we have a point and can find the slope.
Point slope:[tex]y-y_1=m(x-x_1)[/tex]
We must find the slope using the slope formula.
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute [tex]x_1=4\\y_1=9[/tex] and [tex]x_2=-3\\y_2=6[/tex]
[tex]m=\frac{6-9}{-3-4}[/tex]
[tex]m=\frac{6-9}{-3-4}=\frac{-3}{-7} =\frac{3}{7}[/tex]
[tex]m\neq \frac{3}{7}[/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{7}{3}[/tex].
We will substitute [tex]m=-\frac{7}{3}[/tex] and [tex]x_1=14\\y_1=8[/tex].
[tex]y-8=-\frac{7}{3} (x-14)[/tex]
This is the equation of the line perpendicular to the equation line through the points given that crosses through (14,8).
