Question

write an equation for the line that is perpendicular to the given line and passes through the given point y-3=8/3(x+2);(-2,3)

Answer 1

Answer:

$y-3=-\frac{3}{8} (x+2)$

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:$y-y_1=m(x-x_1)$

$m\neq \frac{8}{3}$ in our new equation because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is $m=-\frac{3}{8}$.

We will substitute $m=-\frac{3}{8}$ and $x_1=-2\\y_1=3$.

$y-3=-\frac{3}{8} (x-(-2))$

$y-3=-\frac{3}{8} (x+2)$

This is the equation of the line perpendicular to the equation given that crosses through (-2,3).