Question

The equation for line p is y=2x–7. Line n is perpendicular to line p and passes through the point (

–
4,5). What is the y-intercept of line n?

Answer 1

Explanation:

y=2x-7 has slope, m, =2...a line perpendicular to it would have a slope of -1/2 since perpendicular lines have opposite, reciprocal slopes.

so we have a new m=-1/2 and it passes through the point (4,5) so we can write an equation in point slope form of y - y1 = m(x - x1). We plug -1/2 in for m, 4 in for x1, and 5 in for y1 to get

y-5=-1/2(x-4)

now we distribute the slope to get y-5=-1/2x + 2

now we add 5 to both sides to get the slope intercept equation of

y = -1/2x + 7

now you can see the new y-intercept "b" of the perpendicular equation would be 7 or b = 7