# The equation for the line passing through the origin and is also parallel to line 3 x + 15 y = 22 ### 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 127RE
To determine

## To calculate:The equation for the line passing through the origin and is also parallel to line 3x+15y=22

Expert Solution

The equation for the line passing through the origin and is also parallel to line 3x+15y=22 is y=15x

### Explanation of Solution

Given information:

A line passing through origin (0,0) and parallel to line 3x+15y=22

Formula used:

Slope m of the line passing through two points in general say P1=(x1,y1) and P2=(x2,y2) is:

m=y2y1x2x1

Slope-intercept equation for a given line which has slope as m and y −intercept as b is:

y=mx+b

Two-intercept equation for a given line which has x -intercept as a and y −intercept as b is:

xa+yb=1

When two lines are perpendicular then the product of their slopes is zero that is m1.m2=1

When two lines are parallel then their slope are equal that is m1=m2

Calculation:

Consider theline 3x+15y=22

Recall the slope-intercept equation for a given line which has slope as m and y −intercept as b is:

y=mx+b

Let the line 3x+15y=22 has the general form:

y=m1x+b1

Where m1 is the slope and b1 is the y -intercept of the line.

Now, we try to express the line 3x+15y=22 in the same form:

3x+15y=2215y=3x+22y=315x+2215y=15x+2215

Therefore,

m1=15

Now let the line given parallel to 3x+15y=22 has its general form to be y=m2x+b2

Where m2 is the slope and b2 is the y -intercept of the line.

Recall when two lines are parallel then their slope are equal that is m1=m2

Hence, m2=15

Therefore, equation of the required line reduces to:

y=15x+b2 (1)

Also it is given that this line passes through origin, therefore, it must satisfy (0,0)

That is:

0=315(0)+b2b2=0

Hence, (1) reduces to:

y=15x+0y=15x

Hence, the equation for the line passing through the origin and is also parallel to line 3x+15y=22 is y=15x

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