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

`y-3=-(3)/(8) (x+2)`

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\\eq (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=-(3)/(8)`.

We will substitute
`m=-(3)/(8)` and
`x_1=-2\\y_1=3`.

`y-3=-(3)/(8) (x-(-2))`

`y-3=-(3)/(8) (x+2)`

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