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Chapter 3: Q 208. (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:4x-3y=5Point:(-3,2)

Short Answer

Expert verified

The equation in slope-intercept form:

y=-43x-2

Step by step solution

01

Step 1. Given Data

Line:4x-3y=5Point:(-3,2)

02

Step 2. Find the slope of the given line.

The line is in slope-intercept form:

4x-3y=5-3y=-4x+5y=43x-53y=mx+cWecansee,m=34

03

Step 3. Find the slope of the perpendicular line.

The slopes of Perpendicular lines are negative reciprocals.

Therefore,

m鈯�=-134=-43m鈯�=-43

04

Step 4. Point slope form. 

The given point is:(-3,2)

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

y-y1=m(x-x1)y-2=-43(x-(-3))y-2=-43(x+3)y-2=-43x-4

05

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

Slope-interceptform:y-2=-43x-4y=-43x-4+2y=-43x-2

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