What is an equation of the line that passes through the point (-2,7) and is perpendicular to the line x-4y=24

Question

What is an equation of the line that passes through the point (-2,7) and is perpendicular to the line x-4y=24

Answer 1

solve for y

x-4y =24

-4y = 24-x

y = x/4 - 6 slope = 1/4, the coefficient of the x term

a perpendicular line has the negative inverse, change the sign and flip the fraction upside down to get -4/1 or -4

y=-4x + b. plug in the point x=-2, y=7 to calculate b the y intercept

7=-4(-2) + b

b = 7-8 =-1

y=-4x -1 is the perpendicular line through (-2,7)

general equation in slope intercept form is y=mx +b. m=-4, b=-1