# The equation for the line passing through ( 5 , 2 ) and is also parallel to the line which passes through the points ( − 1 , − 3 ) and ( 3 , 2 ) . ### 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 128RE
To determine

## To calculate:The equation for the line passing through (5,2) and is also parallel to the line which passes through the points (−1,−3) and (3,2) .

Expert Solution

The equation for the line passing through (5,2) and is also parallel to the line which passes through the points (1,3) and (3,2) is 5x4y=17

### Explanation of Solution

Given information:

A line passing through (5,2) and also parallel to the line which passes through the points (1,3) and (3,2)

Formula used:

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

m=y2y1x2x1

Point-slope equation for a given line passing along point P1=(x1,y1) is:

yy1=m(xx1)

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

y=mx+b

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

Calculation:

Consider thepoints (1,3) and (3,2)

Let the slope of the line passing through these points be m1

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

m=y2y1x2x1

To proceed further the following must be known:

x1=1x2=3y1=3y2=2

Therefore,

m1=2(3)3(1)m1=54

Now let the line given parallel tothe line which passes through the points (1,3) and (3,2) has slope m2

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

Hence, m2=54

Now, Recall thePoint-slope equation for a given line passing along point P1=(x1,y1) is:

yy1=m(xx1)

We are given that the required line passes through the point (5,2)

Therefore,

x1=5y1=2

And

m2=m=54

Pitting all the values, the required equation for the line is:

54=y2x55(x5)=4(y2)5x25=4y85x4y=8+255x4y=17

Hence, theequation for the line passing through (5,2) and is also parallel to the line which passes through the points (1,3) and (3,2) is 5x4y=17

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!