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Chapter 3: Q 206. (page 293)

In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope-intercept form.

Line:y=23x-4Point:(2,-4)

Short Answer

Expert verified

The equation in slope-intercept form:

y=-32x-1

Step by step solution

01

Step 1. Given Data

Line:y=23x-4Point:(2,-4)

02

Step 2. Find the slope of the given line.

The line is in slope-intercept form:

y=23x-4y=mx+cWecansee,m=23

03

Step 3. Find the slope of the perpendicular line.

The slopes of Perpendicular lines are negative reciprocals.

Therefore,

m鈯�=-123=-32m鈯�=-32

04

Step 4. Point slope form. 

The given point is:(2,-4)

Substitute the values in the point-slope form which is:

y-y1=m(x-x1)y-(-4)=-32(x-2)y+4=-32(x-2)y+4=-32x+3

05

Step 5. Write the equation in slope-intercept form.

Slope-interceptform:y+4=-32x+3y=-32x+3-4y=-32x-1

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