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Page 2 of 6

When you are given two points, but do not know the

POINT-SLOPE FORM

y-intercept, you should first use the point-slope form to write the equation of the

line that passes through the points, as in Example 2.

Write an Equation of a Line Given Two Points

EXAMPLE

2

Write in slope-intercept form the equation of the line that passes through the

points (3,

2) and (6, 0).

Solution

Find

the slope. Use

(x

,

y

)

(3,

2) and

(x

,

y

)

(6, 0).

1

1

2

2

y

y

2

1

m

Write formula for slope.

x

x

2

1

0

(

2)

Substitute.

6

3

2

Simplify.

3

Write

the equation of the line. Use point-slope form, because you do not

know the y-intercept.

y

y

m(x

x

)

Write point-slope form.

1

1

2

2

y

( 2)

(x

3)

Substitute

for m, 3 for x

, 2 for y

.

3

3

1

1

2

y

2

x

2

Simplify and use distributive property.

3

2

y

x

4

Subtract 2 from each side.

3

2

The equation of the line is y

x

4.

ANSWER

3

CHECK

You can check your

y

answer by graphing.

1

(6, 0)

Notice that the graph of

1

1

3

7

x

2

1

y

x

4 passes

3

(3,

2)

through (3,

2) and (6, 0).

3

2

y

x

4

You can also check your

3

(0,

4)

answer using substitution.

5

Write an Equation of a Line Given Two Points

Write in slope-intercept form the equation of the line that passes through

the given points. Check your answer.

2.

(2, 3) and (4, 7)

3.

( 4, 5) and (2, 2)

4.

(1,

1) and (4,

4)

286

Chapter 5 Writing Linear Equations

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