# The equation for the line with give points ( − 1 , − 6 ) and ( 2 , − 4 ) .

### 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 123RE
To determine

## To calculate:The equation for the line with give points (−1,−6) and (2,−4) .

Expert Solution

The equation for the line with give points (1,6) and (2,4) is 3y2x+16=0

### Explanation of Solution

Given information:

Two points P1=(1,6) and P2=(2,4)

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)

Calculation:

Consider thetwo given points P1=(1,6) and P2=(2,4)

Then in order to proceed following should be known:

x1=1y1=6x2=2y2=4

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

m=y2y1x2x1

Therefore,

m=4(6)2(1)m=23

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

yy1=m(xx1)

Putting the values to get:

y(6)=23(x(1))y+6=23(x+1)3(y+6)=2(x+1)3y+18=2x+23y2x+16=0

Hence, the equation for the line with give points (1,6) and (2,4) is 3y2x+16=0

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