# The equation of line through given conditions.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 20T

(a)

To determine

## To find: The equation of line through given conditions.

Expert Solution

The equation of parallel line is 3x+y3=0 .

### Explanation of Solution

Given:

The coordinates of point is (3,6) and parallel to the line is,

3x+y10=0

Formula used:

The formula of slope-intercept form of line is,

y=mx+b

Where

m is slope of line.

b is y-intercept of line.

Calculation:

Solve the given line in slope-intercept form.

y=3x+10 .

Compare the above equation with formula to get the value of slope that is,

m=3 .

Two non-vertical lines are parallel if their slopes are equal so that the slope of parallel line is also 3 .

The point-slope formula of line is,

yy1=m(xx1) .

Substitute 6 for y1 , 3 for x1 and 3 for m in the above equation to get the equation of line,

y(6)=3(x3)y+6=3x+93x+y3=0

Thus, the equation of parallel line is 3x+y3=0 .

(b)

To determine

### To find: The equation of line through given conditions.

Expert Solution

The equation of line is 2x+3y12=0 .

### Explanation of Solution

Given:

The x-intercept of line is 6 and y-intercept is 4.

Calculation:

The intercepts give the two points of line that is (6,0) and (0,4) .

The formula to find the slope of line passes through two given points is,

m=y2y1x2x1 .

In the above formula (x1,y1) and (x2,y2) are two points of line.

Substitute 4 for y2 , 0 for y1 , 0 for x2 and 6 for x1 in above equation to get the slope of line,

m=4006m=46m=23

Use the point-slope form to get the equation of line, and the formula is,

yy1=m(xx1) .

Substitute 0 for y1 , 6 for x1 and 23 for m to get equation for line,

y0=23(x6)3y0=2x+122x+3y12=0

Thus, the equation of line is 2x+3y12=0 .

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