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Chapter 3: Q 3.61. (page 288)

Find an equation of a line perpendicular to the line y=3x+1that contains the point (4,2). Write the equation in slope-intercept form.

Short Answer

Expert verified

The equation isy=-13x+103.

Step by step solution

01

Step 1. Find the slope of the given line

The given line is: y=3x+1

The line is in slope-intercept form. Therefore, its slope is:

m=3

02

Step 2. Find the slope of the perpendicular line and identify the point

The slopes of perpendicular lines are negative reciprocals.

Therefore, the slope of the perpendicular line is:

m1=-13

And the given point is (4,2).

(x1,y1)=(4,2)

03

Step 3. Substitute the values into the point-slope form

The point-slope form is:

y-y1=m(x-x1)y-2=-13(x-4)y-2=-13x+43

04

Step 4. Write the equation in slope-intercept form.

The slope-intercept form of the perpendicular line is y=-13x+103.

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