Question

What is an equation of the line that is perpendicular to y-3 =-4(x+2)​

Answer 1

`y=(1)/(4) x+c` where
`c` can be any number.

Explanation:

First we need to clear for y:

`y-3 =-4(x+2)\\y=-4(x+2)+3\\y=-4x-8+3\\y=-4x-5`

and now we have an equation of the form:

`y=mx+b`

where m is the slope and b is the y-intercept.

in this case
`m=-4` and
`b=-5`

to find and equation perpendicular to this line, the following must be true:
`m*m_(1)=-1`

where m is the slope of the original line that i just mentioned, and
`m_(1)` is the slope of the new line. Substituting
`m=-4`

`-4*m_(1)=-1`

clearing for
`m_(1)`

`m_(1)=(-1)/(-4) \\m_(1)=(1)/(4)`

thus, the new perpendicular line must have the form:

`y=m_(1)x+c\\y=(1)/(4)x+c`

where the y-intecept
`c` can be any number, some examples are:

`y=(1)/(4)x+3\\y=(1)/(4)x-8`

and so on, the important thing to be a perpendicular line is that the slopes are related to the equation
`m*m_(1)=-1`.

Answer 2

`y - 3 = (1)/(4)(x+2)` or choose any line with slope 1/4

Explanation:

The slope of this line is -4. The slope of the line perpendicular to this line will be the negative reciprocal or 1/4.

Write the equation using the slope m=1/4 and the point slope form.

`y-y_1=m(x-x_1)\\y-3=(1)/(4)(x+2)`

This is the equation of the line that is perpendicular and passes through the same point (-2,3) as the equation listed.