Question

Write the slope-intercept equation of the line perpendicular to y = 5/2 x - 2, which passes though the point (0, 2).
y = 5x + 2
y = -2/5x + 2
y = 2x + 5
y = 1/2x + 5
Write the slope-intercept equation of the line perpendicular to y = 5/2 x - 2, which passes though the point (0, 2).
y = 5x + 2
y = -2/5x + 2
y = 2x + 5
y = 1/2x + 5 @Mathematics

Answer 1

Perpendicular lines have a slope that is negative and reciprocal to the slope of the line to which it is perpendicular.

So in this case, the original line has a slope of 5/2, so the perpendicular line's slope will be (5/2)*-1=(-5/2), then do 1/(-5/2) to reciprocate, and you get -2/5 as the perpendicular slope.

Answer 2

Now for the intercept...

Answer 3

This new line must pass through the point (0,2). So using this equation:
y=mx+b
where m is the slope, b is the intercept, and x,y are the x,y coordinates.

Plug in the given coordinates and calculated slope and solve for b:
2=(-2/5)(0)+b
2=b

So the final equation will be:
y=(-2/5)x+2
(the second answer provided)