Lesson 6-5 Point-Slope Form And Writing Linear Equations Worksheet With Answers Page 4
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1
2
3
4
5
63. Practice
Quick Check
5
5
Working Outdoors
Is the relationship shown by the data
in the table linear? If it is, model the
Temperature
Calories Burned per Day
data with an equation.
Assignment Guide
68ºF
3030
Yes; answers may
62ºF
3130
vary. Sample:
1
A B
1-30, 36-53, 56-59
50
y – 3030 ≠ – (x – 68)
56ºF
3230
3
50ºF
3330
2
A B
31-35, 54, 55, 60
C
Challenge
61-64
In Example 5 you could rewrite y - 206.6 = -1.8(x - 3) as y = -1.8x + 212.
This form gives you useful information about the y-intercept. For instance, 2128F is
Test Prep
65-69
the boiling point of water at sea level.
Mixed Review
70-81
Here are the three forms of linear equations you have studied.
Homework Quick Check
To check students’ understanding
Key Concepts
Summary
Linear Equations
of key skills and concepts, go over
Exercises 18, 34, 40, 55, 57.
Slope-Intercept Form
Standard Form
Point-Slope Form
y = mx + b
Ax + By = C
(y - y
) = m(x - x
)
Error Prevention!
GO
for Help
1
1
m is the slope and b
A and B are
(x
, y
) lies on the
Exercises 19–30
Suggest to
1
1
For more help with
is the y-intercept.
not both 0.
graph of the equation,
students that they circle the
the three forms of a linear
and m is the slope.
x-coordinates and box the
equation, see page 342.
Examples
y-coordinates.
2
5
2
y = - x +
2x + 3y = 5
y - 1 = - (x - 1)
3
3
3
EXERCISES
For more exercises, see Extra Skill and Word Problem Practice.
Practice and Problem Solving
Practice and Problem Solving
GPS
Guided Problem Solving
L3
A
A
Practice by Example
L4
Enrichment
Graph each equation.
1–9. See back of book.
3
L2
Reteaching
1. y - 2 = (x - 3)
2. y - 2 = 2(x - 3)
3. y - 2 =
2
(x 2 3)
Example 1
2
Adapted Practice
L1
2
(page 337)
4. y + 5 = -(x - 2)
5. y + 1 =
(x 1 4)
6. y - 1 = -3(x + 2)
for
3
Practice
L3
GO
Name
Class
Date
Help
7. y + 3 = -2(x - 1)
8. y - 4 = (x - 5)
9. y - 2 = 3(x + 2)
Practice 6-4
Point-Slope Form and Writing Linear Equations
Write an equation in point-slope form for the line through the given points
or through the given point with the given slope.
2. (-2, 3); m = -1
4. (-2, 3); m = 4
1. (5, 7), (6, 8)
3. (1, 2), (3, 8)
3
2 4
Example 2
Write an equation in point-slope form for the line through the given point that has
5. (4, 7); m =
6. (6, -2); m =
7. (0, 5), (-3, 2)
8. (8, 11), (6, 16)
2
3
9. (4, 2), (-4, -2)
11. (0, -7); m = -4
10. (15, 16), (13, 10)
12. (-3, 4), (1, 6)
2 1
the given slope.
10–18. See margin.
(page 337)
13. (1, 2); m undefined
14. (-6, 7); m =
15. (21, -2), (27, 2)
16. (7, 5); m = 0
2
3
17. (8, -2), (14, 1)
20. (6, 2); m =
18. (4, 8), (2, 12)
19. (-5, 13), (-10, 9)
4
5
5
4
21. (5, -3); m = -2
22. (4, 3.5); m = 0.5
23. (-6, 2); m =
24. (100, 90), (80, 120)
3
10. (3, -4); m = 6
11. (4, 2); m =
2
12. (0, 2); m =
5
2 5
25. (-3, 6), (3, -6)
27. (2, 7); m =
28. (-9, 8); m =
26. (11, 7), (9, 3)
3
2
3
5
Is the relationship shown by the data linear? If it is, model the data
with an equation.
3
29.
x
y
30.
x
y
31.
x
y
32.
x
y
13. (-2, -7); m =
2
14. (4, 0); m = 1
15. (5, -8); m = -3
-3
-4
-2
2
3
4
12
5
2
-1
-1
-5
3
7
6
8
3
4
11
1
7
5
-4
7
-13
1
2
-8
-21
5
15
3
10
10
11
16. (-5, 2); m = 0
17. (1, -8); m =
2
18. (-6, 1); m =
5
3
33.
34.
35.
36.
x
y
x
y
x
y
x
y
-6
-5
-6
-7
-3
-4
11
1
-2
1
-3
9
-5
0
2
4
-1
0
4
6
3
3
6
6
Example 3
A line passes through the given points. Write an equation for the line in point-
-3
8
16
15
3
7
14
10
Write an equation of each line in point-slope form.
slope form. Then rewrite the equation in slope-intercept form.
19–30. See margin.
(page 337)
37.
38.
39.
3
2
2
1
1
2
1
1
1 2
2
1
1 2
21. (4, -2), (9, -8)
1
19. (-1, 0), (1, 2)
20. (3, 5), (0, 0)
1
1 2 3 4 5 6
2
3
22. (6, -4), (-3, 5)
23. (-1, -5), (-7, -6)
24. (-3, -4), (3, -2)
25. (2, 7), (1, -4)
27. (3, -8), (-2, 5)
26. (-2, 6), (5, 1)
13
1
Q 1 2
3
27. y ± 8 ≠ – (x – 3);
1,
,
, 2
,
2
, 4
Q
2 R
R
Q
R
28.
(3, 2)
29.
30. (0.2, 1.1), (7, 3)
5
2
13
1
y ≠ – x –
5
5
1
3
28. y –
≠ (x – 1);
339
Lesson 6-5
Point-Slope Form and Writing Linear Equations
2
4
3
1
y ≠ x –
4
4
6
1
25. y – 7 ≠ 11(x – 2);
21. y ± 2 ≠ – (x – 4);
23. y ± 5 ≠ (x ± 1);
1
29. y – 2 ≠ –1(x – );
5
6
2
y ≠ 11x – 15
6
14
1
29
y ≠ – x ±
y ≠ x –
5
y ≠ –x ±
5
5
6
6
2
5
26. y – 6 ≠ – (x ± 2);
1
7
22. y ± 4 ≠ –1(x – 6);
24. y ± 4 ≠ (x ± 3);
1.9
30. y – 1.1 ≠
(x – 0.2);
3
5
4
6.8
y ≠ – x ± 4
y ≠ –x ± 2
1
7
7
y ≠ x – 3
1.9
7.1
3
y ≠
x ±
6.8
6.8
339
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