The Point-Slope Form Worksheet With Answer Key Page 3
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7192
(4–36)
Chapter 4 Linear Equations in Two Variables and Their Graphs
E X A M P L E
3
Writing an equation given a point and a parallel line
Write the equation of the line that is parallel to the line 3x
y
9 and contains the
point (2,
1). Give the answer in slope-intercept form.
Solution
We want the equation of the line through (2,
1) that is parallel to 3x
y
9, as
shown in Fig. 4.26. First write 3x
y
9 in slope-intercept form to determine its
slope:
3x
y
9
y
3x
9
y
5
4
y = – 3x + 9
3
Slope – 3
2
1
– 3
– 2
– 1
x
1
4 5
– 1
(2, – 1)
– 2
– 3
F I G U R E 4 . 2 6
The slope of 3x
y
9 and any line parallel to it is
3. So we want the equation
of the line that has slope
3 and contains (2,
1). Use the point-slope form:
y
y
m(x
x
)
c a l c u l a t o r
Point-slope form
1
1
y
( 1)
3(x
2)
Substitute.
y
1
3x
6
Simplify.
c l o s e - u p
y
3x
5
Slope-intercept form
Graph y
3x
9 and y
The line y
3x
5 has slope
3 and contains the point (2,
1). Check that
I
3x
5 as follows:
(2,
1) satisfies y
3x
5.
10
Perpendicular Lines
– 10
10
1
In Section 4.2 you learned that lines with slopes m and
(for m
0) are perpen-
m
dicular to each other. For example, the lines
– 10
1
Because the lines look paral-
y
2x
7
and
y
x
8
lel and y
3x
5 goes
2
through (2,
1), this graph
are perpendicular to each other. In the next example we will write the equation of a
supports the answer to Exam-
line that is perpendicular to a given line and contains a given point.
ple 3.
E X A M P L E
4
Writing an equation given a point and a perpendicular line
Write the equation of the line that is perpendicular to 3x
2y
8 and contains the
point (1,
3). Write the answer in slope-intercept form.
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