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2.4

Write Equations of Lines

Before

You graphed linear equations.

Now

You will write linear equations.

Why?

So you can model a steady increase or decrease, as in Ex. 51.

Key Vocabulary

For Your Notebook

KEY CONCEPT

point-slope form

•

Writing an Equation of a Line

Given slope m and y-intercept b

Use slope-intercept form:

y 5 mx 1 b

Given slope m and a point (x

, y

)

Use point-slope form:

1

1

y 2 y

5 m(x 2 x

)

1

1

Given points (x

, y

) and (x

, y

)

First use the slope formula to find m.

1

1

2

2

Then use point-slope form with either

given point.

E

1

Write an equation given the slope and y-intercept

X A M P L E

Write an equation of the line shown.

y

2

4

Solution

3

From the graph, you can see that the slope is m 5

}

3

x

1

4

and the y-intercept is b 5 22. Use slope-intercept

(0, 22)

form to write an equation of the line.

y 5 mx 1

b

Use slope-intercept form.

3

3

y 5

x 1 (22)

Substitute

for m and

2

2 for b.

}

}

4

4

3

y 5

x 2 2

Simplify.

}

4

at

✓

G

P

for Example 1

UIDED

RACTICE

Write an equation of the line that has the given slope and y-intercept.

3

7

1.

m 5 3, b 5 1

2.

m 5 22, b 5 24

3.

m 5 2

, b 5

}

}

4

2

98

Chapter 2 Linear Equations and Functions

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