The Point-Slope Form Worksheet With Answer Key Page 4
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4.4 The Point-Slope Form
Solution
y
First graph 3x
2y
8 and a line through (1,
3) that is perpendicular to
3
3x
2y
8 as shown in Fig. 4.27. The right angle symbol is used in the figure to
3x + 2y = 8
2
indicate that the lines are perpendicular. Now write 3x
2y
8 in slope-intercept
1
form to determine its slope:
x
– 3
– 2
– 1
1 2
4
– 1
3x
2y
8
– 2
2y
3x
8
– 3
(1, – 3)
2
3
Slope
—
3
Slope
– —
3
y
x
4
Slope-intercept form
2
– 5
2
F I G U R E 4 . 2 7
3
2
The slope of the given line is
. The slope of any line perpendicular to it is
. Now
2
3
2
we use the point-slope form with the point (1,
3) and the slope
:
c a l c u l a t o r
3
y
y
m(x
x
)
Point-slope form
1
1
2
c l o s e - u p
y
( 3)
(x
1)
3
Graph y
(2 3)x
11 3 and
2
2
1
y
( 3 2)x
4 as shown:
y
3
x
2
3
3
10
2
2
y
x
3
Subtract 3 from each side.
3
3
– 15
15
2
1
1
y
x
Slope-intercept form
3
3
– 10
Because the lines look perpen-
2
1
1
So y
x
is the equation of the line that contains (1,
3) and is perpendicu-
dicular and y
goes through
3
3
1
I
2
1
1
lar to 3x
2y
8. Check that (1,
3) satisfies y
x
.
(1,
3), the graph supports
3
3
the answer to Example 4.
W A R M - U P S
True or false? Explain your answer.
1. The formula y
m(x
x
) is the point-slope form for a line.
1
2. It is impossible to find the equation of a line through (2, 5) and ( 3, 1).
3. The point-slope form will not work for the line through (3, 4) and (3, 6).
4. The equation of the line through the origin with slope 1 is y
x.
5. The slope of the line 5x
y
4 is 5.
1
6. The slope of any line perpendicular to the line y
4x
3 is
.
4
7. The slope of any line parallel to the line x
y
1 is
1.
8. The line 2x
y
1 goes through the point ( 2,
3).
9. The line is 2x
y
4 and y
2x
7 are parallel.
10. The equation of the line through (0, 0) perpendicular to y
x is y
x.
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