# 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 22E
To determine

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

Expert Solution

The equation of the line is y=23x+6.

### Explanation of Solution

Given:

The required line is passing through y intercept 6 and parallel to 2x+3y+4=0.

Property used:

Two non-vertical lines are parallel if and only if they have the same slope.

The equation of the line with slope m and y intercept b is, y=mx+b.

Calculation:

To find the slope, rewrite the equation,

2x+3y+4=03y=2x4y=23x43y=mx+b

Therefore, m=23.

Substitute the values in the property mentioned above.

m=23, b=6Therefore,y=23x+6

Thus, the equation of the line is y=23x+6.

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