# The equation for the line passing through a given point ( 6 , − 3 ) and having slope − 1 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 124RE
To determine

## To calculate:The equation for the line passing through a given point (6,−3) and having slope −12

Expert Solution

The equation for the line passing through (6,3) and having slope 12 is 2y+x=0

### Explanation of Solution

Given information:

Point P1=(1,6) and slope m=12

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 thepoint P1=(1,6) and slope m=12

Then in order to proceed following should be known:

x1=6y1=3

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(3)=12(x6)y+3=12(x6)2(y+3)=1(x6)2y+6=x+62y+x=0

Hence, the equation for the line passing through (6,3) and having slope 12 is 2y+x=0

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