Question

Write an equation of the line that passes through (2,-4) and is perpendicular to the line

y = -2x + 5 in slope intercept form

Answer 1

y = (1/2)x - 5

Explanation:

The slope of the line y = -2x + 5 is -2. The slope of any straight line perpendicular to this line is therefore the negative reciprocal of -2, which comes out to +1/2.

Using this fact, and the point (2, -4), we write out the slope-intercept form y = mx + b, and substitute the appropriate values:

-4 = (1/2)(2) + b

Then:

-4 = 1 + b, which yields b = -5

Thus, the desired equation is y = (1/2)x - 5