Find an equation of the line that satisfies the given conditions. Through (−3, −9); perpendicular to the line passing through (0, 3) and (4, 1)
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
x2 = 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.