# 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 21E
To determine

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

Expert Solution

The equation of the line is y=34x6.

### Explanation of Solution

Given:

The required line is passing through the points (1,6) and parallel to x+2y=6.

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.

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,

x+2y=62y=6xy=6212xy=12x+3y=mx+b

Therefore, m=12.

Substitute the values in the above mentioned property,

yy1=m(xx1)y(6)=12(x1)y+6=12(x1)y+6=12x+12y=12x+126y=12x+(126×22)y=12x+(12122)y=12x112

Thus, the equation of the line is y=12x112.

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