# The equation of the line for the given conditions. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter B, Problem 24E
To determine

## To find: The equation of the line for the given conditions.

Expert Solution

The equation of the line is y=2x+13.

### Explanation of Solution

Given:

The required line is passing through the points (12,23) and parallel to 4x8y=1.

Property used:

Two lines with slopes m1 and m2 are perpendicular if and only if m1m2=1 their slopes are negative reciprocal m2=1m1.

The equation of the line passes through the point (x1,y1) and having slope m is, yy1=m(xx1).

Calculation:

To find the slope, rewrite the equation,

4x8y=18y=4x+18y=4x1y=48x18y=12x18y=mx+b

Therefore, the slope becomes,

m1=12m2=1m1m2=1(12)m2=2.

Substitute the values in the property mentioned above.

yy1=m(xx1)y(23)=(2)(x12)y+23=2x+22y+23=2x+1

On further simplification the equation becomes,

y=2x+123y=2x+1×3323y=2x+13

Thus, the equation of the line is y=2x+13.

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