Question

The equation of a line is y=-5x+2. What is the y-intercept of a perpendicular line that travels through the point ( 10, 10).

Answer 1

8

Explanation:

We can construct an equation by using y=mx+c, where m is the gradient (slope) and c is the y-intercept. The y-intercept is the point where x is 0.

One of the properties of perpendicular lines in a graph is that their gradient is the negative reciprocal (-1/m). the equation of the other line is already in the form of y=mx+c, y= -5x + 2, so the gradient of the line whose y-intercept is to be found is -1/-5=1/5.

Next just put the new gradient in place of m in the question:

y= (1/5)x+ c

Plug in the coordinates in place of x and y and rearrange for c:

10= (1/5)(10) + c

c= 8