finding the slope of a perpendicular line

Question

Find the slope of a line perpendicular to the line whose equation is 2y+6x=64?

Answer 1

Given line 2y+6x = 64

Subtract 6x from each side.

2y+6x-6x = 64-6x

2y = -6x+64

Divide to each side by 2.

2y/2 = (-6/2)x+64/2

y = -3x+32

Slope of the given line say m1 = -3

Slope of perpendicular line say m2 .

We know that m1*m2 = -1

m2 = 1/3

Required slope of the line is 1/3.

Answer 2

The line equation is 2y + 6x = 64.

Write the equation in slope-intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

2y = - 6x + 64

y = (- 6/2)x + (64/2)

y = - 3x + 32.

Compare the equation with slope-intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

Slope (m) = - 3.

Because the slopes of perpendicular lines are negative reciprocals, the slope of perpendicular line is 1/3.