Collge Alegegra

Question

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line.

 Point: (-4,9)

Line: 6x - 30y=6

Answer 1

6x - 30y = 6

-30y = -6x + 6

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

This line has a slope of 1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the new line will have a slope of -5.

 

P(-4,9)

Now use the Point-Slope form of the equation of a line.

y - y₁ = m(x - x₁)

y - 9 = -5(x + 4)

y - 9 = -5x - 20

y = -5x - 11

 

 

Answer 2

6x - 30y = 6

-30y = -6x + 6

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

 

Perpendicular lines have opposite, reciprocal slopes.

 

y - 9 = -5(x - (-4)

y - 9 = -5x - 20

y = -5x - 11

 

Let's check.

 

9 = -5(-4) - 11

9 = 20 - 11

9 = 9

0 = 0

 

Check.