# 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 23E
To determine

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

Expert Solution

The equation of the line is y=52x+12.

### Explanation of Solution

Given:

The required line is passing through the points (1,2) and parallel to 2x+5y+8=0.

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,

2x+5y+8=05y=2x8y=25x85y=mx+b

Therefore, the slope becomes,

m1=25m2=1m1m2=1(25)m2=52.

Substitute the values in the property mentioned above.

yy1=m(xx1)y(2)=(52)(x(1))y+2=52(x+1)y+2=52x+52y=52x+522

On further simplification the equation becomes,

y=52x+522×22y=52x+5242y=52x+12

Thus, the equation of the line is y=52x+12.

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