Intermediate Algebra (11th edition)

Writing an Equation of a Line, Given the Slope and a Point

Write an equation of the line with slope and passing through the point

Method 1 Use the point-slope form of the equation of a line, with

and

Point-slope form

Substitute for m, and.

Definition of subtraction

(*) Multiply by 3.

Add 15.

Slope-intercept form Divide by 3.

Method 2 An alternative method for finding this equation uses slope-intercept

form, with and

Slope-intercept form

Substitute for y,m, and x.

Multiply.

Add.

Since and , the equation is y= NOW TRY

1

3 x+

17

b= 3.

17

m= 3

1

3

2

5 = 3

15

3 ;

17

3

= b, or b=

17

3

5 =-

2

3

+b

5 =

1

3

1 - 22 +b

y= m x+b

1 x, y 2 = 1 - 2, 5 2 m= 31.

y=

1

3

x+

17

3

3 y= x+ 17

3 y- 15 = x+ 2

y- 5 =

1

3

1 x+ 22

y- 5 = y 1 , x 1

1

3

3 x- 1 - 224

y- y 1 = m 1 x- x 12

m=^13.

1 x 1 , y 12 = 1 - 2, 5 2

(^131) - 2, 5 2.

EXAMPLE 3

4.2 Systems of Linear Equations in Three Variables

Point-Slope Form

The point-slope formof the equation of a line with slope mpassing through the

point is

Slope

Given point

yy 1 =m 1 xx 12.

1 x 1 , y 12

Solve for b.

OBJECTIVE 4 Write equations of horizontal and vertical lines. A horizon-

tal line has slope 0. Using point-slope form, we can find the equation of a horizontal

line through the point.

Point-slope form

Multiplication property of 0

Add b.

Point-slope form does not apply to a vertical line, since the slope of a vertical line is

undefined. A vertical line through the point 1 a, b 2 has equation x= a.

y= b

y- b= 0

y - b= 01 x-a 2 y 1 =b,m=0,x 1 =a

y- y 1 = m 1 x- x 12

1 a, b 2

NOW TRY
EXERCISE 3
Write an equation of the line
with slope and passing

through the point 1 5, - 32.

• (^15)
  NOW TRY ANSWER

3. y=-^15 x- 2

Same equation

found in Method 1