Question

Find an equation of the line that satisfies the given conditions.
through (2, 4) perpendicular to
x − 4y + 7 = 0

I know that you would set it up as
-4y = -x - 7, but would you divide the 4 to get slope = (1/4)x, which would make the perpendicular slope 4?

Answer 1

Slopes of perpendicular lines are negative reciprocals of each other. One is + , the other is - .

Here is a little trick for perpendicular lines
If we have some line
Ax + By + C = 0

then the line
Bx -Ay + k = 0 is perpendicular, that is just switch the coefficients and make the sign opposite. The constant will probably be different.

So for yours, the new equation must be
4x + y + k = 0
plug in the given point
4(2) + 4 + k = 0
k = -12

4x + y - 12 = 0

now wasn't that easy ?
Took about 3 lines.