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Chapter 4: Q. 131 (page 534)

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

Short Answer

Expert verified

The equation of the line in slope-intercept form isy=-x3+103.

Step by step solution

01

Step 1. Given Information.

The equation of the line,y=3x+1.

The point is,(4,2).

02

Step 2. Finding the slope.

The slope-intercept form is,

y=mx+b.

Comparing the equation of the line y=3x+1,

m1=3

When two lines are perpendicular,

m1脳m2=-1鈬�3脳m2=-1鈬�m2=-13

03

Step 3. Equation of the line.

The point-slope form is,

(y-y1)=m(x-x1)

Inputting the values,

(y-2)=-13(x-4)y-2=-x3+43y=-x3+103

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