What is the equation in slope-intercept form of the line that crosses the x-axis at 4 and is perpendicular to the line represented by y = −2 over 3x + 4?

Question

What is the equation in slope-intercept form of the line that crosses the x-axis at 4 and is perpendicular to the line represented by y = −x + 4?

A

y = −x + 6?

B

y = −x  6

C

y = x + 6

D

y = x  6

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Answer 1

Hi Maria H

D. (3/2)x - 6

If I’ve interpreted your information correctly,

According to your information since the line crosses the x axis at 4 you have the point (4,0), the x intercept, on the line perpendicular to y = −x + 4

Perpendicular lines have inverse slopes with opposite signs since the slope, m of y = −x + 4

is

m = -2/3

The slope of the perpendicular line is

m = 3/2

Your perpendicular line starts as

y = (3/2)x + b

Use the coordinates of the x intercept to solve for b

0 = (3/2)4 + b

0 = 6 + b

-6 = b

Your perpendicular line in Slope Intercept form is

y = (3/2)x - 6

You can graph both lines at Desmos.com to confirm that they are perpendicular, hope this helps