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Chapter 3: Q. 5 (page 176)

Find the equation of the line perpendicular to the line y = 2x + 1 and containing the point (3, 5). Express your answer in slope鈥搃ntercept form and graph the line.

Short Answer

Expert verified

The equation of line isy=-12x+132.

Step by step solution

01

Step 1. Given information.

Find the equation of the line perpendicular to the line y = 2x + 1 and containing the point (3, 5). Express your answer in slope鈥搃ntercept form and graph the line.

02

Step 2. Step 2. Definition.

The equation of line ( in slope - intercept form) is given by:

y=mx+b;m鈮�0

If two directions are vertical, their direction coefficients are inversely proportional:

m2=-1m1

03

Step 3. Equation of line.

Slope:

There is given the equation of line y=2x+1, so the m1=2. The line we are searching for is perpendicular to the given line.

Then m2=-12.

The y - intercept:

The point 3,5is on the, because we want to find b, put the coordinates of the points inside the equation:

y=-12x+b5=-12路3+b5=-32+bb=5+32b=132

So, the equation of line is :

y=-12x+132y

04

Step 4. Conclusion.

The equation of line isy=-12x+132y.

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