Question

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

Answer 1

Answer:

$y=\frac{1}{4} x+c$   where $c$ can be any number.

Step-by-step 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 $m_{1}$

$m_{1}=\frac{-1}{-4} \\m_{1}=\frac{1}{4}$

thus, the new perpendicular line must have the form:

$y=m_{1}x+c\\y=\frac{1}{4}x+c$

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

$y=\frac{1}{4}x+3\\y=\frac{1}{4}x-8$

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

Answer:

$y - 3 = \frac{1}{4}(x+2)$ or choose any line with slope 1/4

Step-by-step 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.

$y-y_1=m(x-x_1)\\y-3=\frac{1}{4}(x+2)$

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