Beginning Algebra, 11th Edition

Using the Slope-Intercept Form to Write an Equation

Write an equation, in slope-intercept form, of the line having slope 4 passing through

the point.

Since the line passes through the point we can substitute

and the given slope into and solve for b.

Slope-intercept form

Let and

Multiply.

Subtract 8.

Now substitute the values of mand binto slope-intercept form.

Slope-intercept form

y= 4 x- 3 m= 4 and b=- 3 NOW TRY

y= mx+b

- 3 = b

5 = 8 + b

5 = 4122 + b x=2, y=5, m=4.

y= mx+ b

m= 4 y= mx+b

1 2, 5 2 , x=2, y= 5,

1 2, 5 2

EXAMPLE 5

214 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions

0 , bis the

y-intercept. Don’t

stop here.

1 2

There is another form that can be used to write the equation of a line. To develop

this form, let mrepresent the slope of a line and let represent a given point

on the line. Let represent any other point on the line. See FIGURE 33. Then,

Definition of slope

Multiply each side by

Rewrite.

This result is the point-slope formof the equation of a line.

y-y 1 =m 1 x-x 12.

m 1 x-x 12 =y-y 1 x-x 1.

m=

y-y 1

x-x 1

1 x, y 2

1 x 1 , y 12

x

y

0

Slope is m.

Any other

point (x, y)

Given point

(x 1 , y 1 )

FIGURE 33

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

Using the Point-Slope Form to Write Equations

Write an equation of each line. Give the final answer in slope-intercept form.

(a)Through with slope

The given point is so and Also,

Point-slope form

Let

Definition of subtraction

Distributive property

y=- 3 x- 2 Add 4.

y- 4 =- 3 x- 6

y- 4 =- 31 x+ 22

y - 4 = - 33 x- 1 - 224 y 1 =4, m=-3, x 1 =-2.

y- y 1 = m 1 x- x 12

1 - 2, 4 2 x 1 =- 2 y 1 =4. m=-3.

1 - 2, 4 2 , - 3

EXAMPLE 6

Only y 1 , m, and x 1

are replaced with

numbers.

NOW TRY
EXERCISE 5
Write an equation, in slope-
intercept form, of the line
having slope 3 and passing
through the point 1 - 2, 1 2.

NOW TRY ANSWER
5.y= 3 x+ 7

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