   Chapter 1.4, Problem 46E

Chapter
Section
Textbook Problem

Find an equation of the line that passes through the point (2, 4) and is perpendicular to the line 3x + 4y − 22 = 0.

To determine

To find: The equation of line that passes through the given point and is perpendicular to given line.

Explanation

Given:

The point is (2,4) and perpendicular line 3x+4y22=0 .

Formula used:

The formula to calculate the slope m that passes through the points (x1,y1) and (x2,y2) is,

m=y2y1x2x1 (1)

The L1 and L2 are two distinct non vertical lines that have slopes m1 and m2 , respectively then L1 is perpendicular to L2 if and only if,

m1=1m2 (2)

An equation of line that has slope m and y intercept b is,

y=mx+b (3)

Calculation:

Assume the point (x1,y1)=(2,4) .

Assume L1 be the line which is perpendicular to the line L2 3x+4y22=0 .

Rewrite the equation of perpendicular line into the slope intercept form.

4y=3x+22y=34x+224y=34x+112

Compare the above equation with equation (3) to calculate the slope m2 of line L2 .

m2=34

Since, Slope of lineL1=1Slope of lineL2

Substitute 34 for m2 in equation (2)

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