Question

what is the equation of a line that is perpendicular to y= 1/2x - 6 and passes through the point (6,4)?

Answer 1

Perpendicular to a slope of 1/2 is the negative reciprocal slope -1/(1/2) = -2.

y = - 2 x + b

y + 2 x = b

b = 4 + 2(6) = 16

y = -2x + 16

Check:

-2(6)+16=4 good

Answer: y = -2x + 16

Answer 2

The equation for any straight line is y=mx+b, m being the slope and b being the y-intercept. Because the line is perpendicular to y=1/2x-6, the slope of the two lines is the same. Therefore, m=1/2x. Now we need to find b, which we can do by plugging the given coordinate in. (4=1/2(6)+b) Solve and find b=1. The equation is y=1/2x+1.