If you can please show your work so I can learn from it please! Thank you!
Find the equation of the line. Write the equation using function notation.
Through (-2,4); perpendicular to f(x)=-2x+3
The answer is 1/2x +5 but I dont know how they got that.
Through (6,-6); parallel to 5x+6y=18
the answer is -5/6x-1
I got y=-5/6x-1
My teacher gave me the cheat sheet for the review to make sure when I study that I can correct them.
The first function is f(x) = -2x + 3, so the gradient of that line is -2.
The product of the gradients of perpendicular lines is -1, so that means the gradient of the normal must be 1/2 (since 1/2 x -2 = -1).
So for your normal, so far you have y = (1/2)x + c.
You are given a point that lies on this normal, namely (x, y) = (-2, 4), so substituting this in gives
4 = (1/2) x (-2) + c
4 = -1 + c
5 = c.
Therefore the equation of the normal is y = (1/2)x + 5.
In function notation this is
Now for your second, start by getting your original line in the form y = mx + c.