# Chapter 5 Lesson 5.3 Writing Linear Equations Given Two Points Worksheet Page 2

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.
3
CHECK
You can check your
y
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)
5
Write an Equation of a Line Given Two Points
Write in slope-intercept form the equation of the line that passes through
2.
(2, 3) and (4, 7)
3.
( 4, 5) and (2, 2)
4.
(1,
1) and (4,
4)
286
Chapter 5 Writing Linear Equations