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5.3

5.3

Writing Linear Equations

Given Two Points

Goal

Write an equation of a

How steep is the mountain?

line given two points on

the line.

In this lesson you will learn

to write an equation of a line

Key Words

given any two points on the

• slope

line. In Example 1 you will

• slope-intercept form

write a linear equation that

• point-slope form

models a snowboarder’s

descent down a mountain.

Use a Graph

EXAMPLE

1

The line at the right models a

y

snowboarder’s descent down a

5

mountain. Write the equation

( 4, 5)

of the line in slope-intercept form.

3

(0, 2)

Student Help

Solution

1

x

Find

the slope.

S

T

TUDY

IP

1

7

5

3

1

In Example 1, notice

y

y

5

2

3

that the graph shows

2

1

m

x

x

4

0

4

the y-intercept.

2

1

Because you know the

Write

the equation of the line. From the graph, you can see the y-intercept

y-intercept, use the

is b

2. Use slope-intercept form.

slope-intercept form to

write the equation.

y

mx

b

Write slope-intercept form.

3

3

y

x

2

Substitute

for m and 2 for b.

4

4

3

The equation of the line is y

x

2.

ANSWER

4

Use a Graph

1.

The graph at the right

y

5

models a car’s ascent up a

hill. Write the equation of

(10, 4)

3

the line in slope-intercept

form.

(0, 1)

1

3

5

7

9

11

x

5.3 Writing Linear Equations Given Two Points

285

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Parent category: Education