Lesson 6-5 Point-Slope Form And Writing Linear Equations Worksheet With Answers Page 5
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1
2
3
4
5
64. Assess
Reteach
&
Example 4
Is the relationship shown by the data linear? If so, model the data with an equation.
(page 338)
31.
See left.
32.
See left.
33.
no
x
y
x
y
x
y
31. Yes; answers may
PowerPoint
4
9
10
5
3
1
vary. Sample:
y – 9 ≠ –2(x ± 4)
Lesson Quiz
2
3
2
19
6
4
32. Yes; answers may
5
9
5
40
9
13
vary. Sample:
1. Graph the equation
9
17
11
58
15
49
y – 40 ≠ 3(x – 5)
y + 1 = -(x - 3).
y
34.
35.
no
Example 5
Speed Over Posted
Fine
Volume
Weight
See
4
(page 338)
Speed (mi/h)
($)
(gal)
(lb)
left.
0
0
2
34. Yes; answers may
10
75
vary. Sample:
x
2
16
12
95
y – 75 ≠ 10(x – 10)
O
2
2
4
4
33
15
125
2
6
50
19
165
B
B
Apply Your Skills
Write an equation of each line in point-slope form.
36–53. Answers may vary
2. Write an equation of the line
from point indicated by the equation.
2
with slope - that passes
36.
37.
38.
3
y
y
y
through the point
4
5
x
4
2
O
2
(0, 4).
y – 4 ≠ – (x – 0),
3
2
2
2
or y ≠ – x + 4
3
2
3. Write an equation for the line
x
O
2
x
that passes through
5
2
O
2
4
(3, -5) and (-2, 1) in
3
2
y – 2 ≠ (x – 1)
y ± 3 ≠ (x – 1)
5
y ≠ – (x – 5)
point-slope form and
4
5
7
Write one equation of the line through the given points in point-slope form and
slope-intercept form.
one in standard form using integers.
39–53. See margin.
6
y ± 5 ≠ – (x – 3);
5
40. (6, -3), (-2, -3)
41. (0, 0), (-1, -2)
6
39. (1, 4), (-1, 1)
7
y = – x –
5
5
42. (0, 2), (-4, 2)
43. (-6, 6), (3, 3)
44. (2, 3), (-1, 5)
4. Is the relationship shown by
the data linear? If so, model
45. (5, -3), (3, 4)
47. (-7, 1), (5, -1)
46. (2, 2), (-1, 7)
that data with an equation.
2
48. (-8, 4), (-4, -2)
49. (2, 4), (-3, -6)
50. (5, 3), (4, 5)
yes; y ± 3 ≠ (x – 0)
5
52. (-2, 4), (0, -5)
53. (6, 2), (1, -1)
51. (0, 1), (-3, 0)
x
y
-10
-7
Science
54.
At the surface of the ocean, pressure is 1 atmosphere. At 66 ft below
A scuba diver can
0
-3
descend to about
sea level, the pressure is 3 atmospheres. The relationship of pressure and depth
131 feet.
is linear.
5
-1
1
y ≠ – x ± 1
a. Write an equation for the data.
33
20
5
The sub-
b. Predict the pressure at 100 ft below sea level.
about 4 atmospheres
mersible
Alvin can
55.
Environment
Worldwide carbon monoxide emissions are decreasing about 2.6
descend to
GPS
million metric tons each year. In 1991, carbon monoxide emissions were 79
about 2.5 miles.
Alternative Assessment
million metric tons. Use a linear equation to model the relationship between
carbon monoxide emissions and time. Let x = 91 correspond to 1991.
In 1960, the
Let students work in pairs.
y ≠ –2.6x ± 315.6
submersible Trieste
descended to a
Open-Ended
56. a.
Write an equation in point-slope form that contains the point
Instruct each student to write
record depth of
(-4, -6). Explain your steps.
a–b. See margin.
coordinates for two points, and
6.8 miles.
then write an equation passing
b. How many equations could you write in part(a)? Explain.
through those points in point-
How would the graph of y - 12 = 8(x - 2) change if all of
57.
Critical Thinking
slope form. Have each pair
y-intercept changes
the subtraction signs were changed to addition signs?
exchange points and repeat.
from –4 to 4.
Is y - 5 = 2(x - 1) an equation of a line through (4, 11)? Explain.
58.
Reasoning
Then compare answers to check.
Yes; the point satisfies the equation.
340
Chapter 6
Linear Equations and Their Graphs
pages 307–309 Exercises
1
7
41. y ± 2 ≠ 2(x ± 1);
43. y – 6 ≠ – (x ± 6);
45. y ± 3 ≠ – (x – 5);
3
2
–2x ± y ≠ 0
3
x ± 3y ≠ 12
39. y – 4 ≠ (x – 1);
7x ± 2y ≠ 29
2
42. y – 2 ≠ 0(x – 0);
2
–3x ± 2y ≠ 5
5
44. y – 3 ≠ – (x – 2);
46. y – 2 ≠ – (x – 2);
3
y ≠ 2
3
40. y ± 3 ≠ 0(x – 6);
2x ± 3y ≠ 13
5x ± 3y ≠ 16
y ≠ –3
340
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