Find the equation of the line through (5,7) which is perpendicular to the line y= -x/2-4

Answer 1

y = -x/2 -4

or

y = (-1/2)x - 4 has slope = -1/2.

A perpendicular line has a negative inverse slope = +2

to find the negative inverse, change the sign and flip the fraction upside down, to convert -1/2 to +2/1 = 2

y = mx +b where m=slope = 2, and b = intercept

plug in the point (5,7), x=5, y=7 to solve for b

7 =2(5) + b

b = 7-10 = -3

y = 2x -3 is the perpendicular line through the point (5,7)