The Point-Slope Form Worksheet With Answer Key Page 2
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4
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6
7(4–35)
191
4.4 The Point-Slope Form
Alternate Solution
1
Replace m by
, x by
2, and y by 3 in the slope-intercept form:
2
y
mx
b
Slope-intercept form
1
3
( 2)
b
Substitute m
and (x, y)
( 2, 3).
2
3
1
b
Simplify.
4
b
I
1
Since b
4, we can write y
x
4.
2
The point-slope form can be used to find the equation of a line
C A U T I O N
for any given point and slope. However, if the given point is the y-intercept, then it
is simpler to use the slope-intercept form.
E X A M P L E
2
Writing an equation given two points
Find the equation of the line that contains the points ( 3,
2) and (4,
1), and
write it in standard form.
Solution
First find the slope using the two given points:
c a l c u l a t o r
2
(
1)
1
1
m
3
4
7
7
c l o s e - u p
1
Now use one of the points, say ( 3,
2), and slope
in the point-slope form:
7
Graph y
(x
3) 7
2 to
y
y
m(x
x
)
Point-slope form
1
1
see that the line goes through
1
( 3, 2) and (4, 1).
y
( 2)
[x
( 3)]
Substitute.
7
4
1
y
2
(x
3)
Simplify.
7
– 6
24
1
7(y
2)
7
(x
3)
Multiply each side by 7.
7
7y
14
x
3
– 4
7y
x
11
Subtract 14 from each side.
Note that the form of the
equation does not matter on
x
7y
11
Subtract x from each side.
the calculator as long as it is
x
7y
11
Multiply each side by
1.
solved for y.
The equation in standard form is x
7y
11. Using the other given point, (4, 1),
I
would give the same final equation in standard form. Try it.
Parallel Lines
In Section 4.2 you learned that parallel lines have the same slope. For example, the
lines y
6x
4 and y
6x
7 are parallel because each has slope 6. In the next
example we write the equation of a line that is parallel to a given line and contains
a given point.
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