Find an equation of the line

First you will need to find the slope of the perpendicular line by using the slope formula:

 

(y₂ - y₁) / (x₂ - x₁)

 

Let's say that (0,3) is the first point and (4,1) is the second point. Therefore:

 

x₁ = 0

x_{2 = 4}

 

y₁ = 3

y₂ = 1

 

Now plug in the numbers:

 

(1 - 3) / (4 - 0) = (-2) / (4) = -1/2

 

Therefore, the slope of the perpendicular line is -1/2. That means the slope of the line we are trying to find is 2 since we take the negative reciprocal (negative reciprocal means you take the number, in this case, -1/2, flip it to get -2 and then take the negative to get, 2, since a negative of a negative is a positive) to find the slope of a line that is perpendicular to another.

 

Now plug in the slope into point slope form which is:

 

y - y₁ = m(x - x₁)

 

Remember, now x₁ and y₁ represent the first point in the problem (-3, -9) since we are trying to find the equation of the line with that point. Also m = slope.

 

Now just plug in the numbers to get:

 

y - -3 = 2(x - -9)

 

This can be simplified to ----> y + 3 = 2(x + 9)

 

Now that answer is acceptable, but if the problem wants you to change it to slope-intercept form then do algebra to isolate the y value. If you need any help with that just comment.