Answer:
x = -3
Step-by-step explanation:
The slope of the line through the given points is ...
m = (change in y)/(change in x) = (2-0)/(4-0) = 1/2
The slope of a perpendicular line will be the negative reciprocal of this:
perpendicular slope = -1/m = -1/(1/2) = -2
The point given on the perpendicular line is its y-intercept, so we can write the equation of the line in slope-intercept form as ...
y = -2x -2
For y=4, the corresponding value of x is the solution to ...
4 = -2x -2
6 = -2x . . . . . . add 2
-3 = x . . . . . . . .divide by -2
The perpendicular line goes through points (0, -2) and (-3, 4).
