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Equations of Lines

•

Write an equation of a line given information

about its graph.

•

Solve problems by writing equations.

Cost of Cellular Service

Vocabulary

can the equation of a

can the equation of a

•

slope-intercept form

line describe the cost of

line describe the cost of

30

•

point-slope form

cellular telephone service?

cellular telephone service?

20

A certain cellular phone company

10

charges a flat rate of $19.95 per month

for service. All calls are charged $0.07

per minute of air time t. The total charge

10

20

30

40

50

C for a month can be represented by the

Minutes

equation C

0.07t

19.95.

WRITE EQUATIONS OF LINES

You may remember from algebra that an

equation of a line can be written given any of the following:

• the slope and the y-intercept,

• the slope and the coordinates of a point on the line, or

• the coordinates of two points on the line.

The graph of C

19.95 has a slope of 0.07, and it intersects the y-axis

0.07t

at 19.95. These two values can be used to write an equation of the line. The

slope-intercept form

of a linear equation is y

mx

b, where m is the slope of

the line and b is the y-intercept.

slope

y

mx

b

C

0.07t

19.95

y-intercept

Slope and y-Intercept

Example

Example

1

1

Write an equation in slope-intercept form of the line with slope of

4

and y-intercept of 1.

y

mx

b

Slope-intercept form

y

4x

1

m

4, b

1

The slope-intercept form of the equation of the line is y

4x

1.

Another method used to write an equation of a line is the point-slope form of a

point-slope form

linear equation. The

is y

y

m(x

x

), where (x

, y

) are the

1

1

1

1

coordinates of any point on the line and m is the slope of the line.

given point

(x

,

y

)

1

1

y

y

m(x

x

)

1

1

slope

Lesson 3-4 Equations of Lines 145

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