5-4 Equations in Point-Slope Form
Name
Date
6
Write the point-slope form of the line with slope 5 that contains
point (⫺4, ⫺2). Then graph the line.
y ⫺ y1 ⫽ m(x ⫺ x1)
6
Plot the point (⫺4, ⫺2).
Use the point-slope form,
where m is the slope and the
point (x1, y1) lies on the line.
Use the slope to locate ⫹6
point (⫺4 ⫹ 5, ⫺2 ⫹ 6),
or (1, 4), on the line.
4
y ⫺ (⫺2) ⫽ 5 [x ⫺ (⫺4)]
Substitute ⫺2 for y1,
6
5 for m, and ⫺4 for x1.
Simplify.
6
y ⫹ 2 ⫽ 5 (x ⫹ 4)
⫹5
y
4
2
x
2
0
Connect the points.
4
2
2
4
Write an equation of a line in point-slope form with the given slope that
passes through the given point. Then graph the line on a separate sheet
of paper. Check students’ graphs.
2
1. slope: ⫺ 3 ; point: (8, 12)
y y1 m(x x1)
2
y1 12, m 3 , x1 8
2
y 12 3 (x 8)
7 6
4. slope: ⫺13; point: (⫺ 2 , 11)
y1 2
4
3. slope: ⫺8; point: ( 3 , ⫺ 5 )
5
y1 15, m , x1 2
2
4
2
y1 , m 8, x1 5
3
5
y 15 (x 2)
2
y
5. slope: 1.4; point: (⫺2.5, 3.5)
4
2
8 x 5
3
(
)
6. slope: 0.7; point: (4.5, ⫺6.5)
7
6
, m 13, x1 2
11
y
Copyright © by William H. Sadlier, Inc. All rights reserved.
5
2. slope: ⫺ 2 ; point: (2, 15)
6
7
13 x 11
2
(
)
y1 3.5, m 1.4, x1 2.5
y 3.5 1.4(x 2.5)
7. slope: 0.5; point: (⫺1.25, 2.75)
8. slope: ⫺0.75; point: (⫺1.5, ⫺3)
y1 2.75, m 0.5, x1 1.25
y 2.75 0.5(x 1.25)
y1 3, m 0.75, x1 1.5
y 3 0.75(x 1.5)
y1 6.5, m 0.7, x1 4.5
y 6.5 0.7(x 4.5)
9. slope: 0.125; point: (⫺4, ⫺8)
y1 8, m 0.125, x1 4
y 8 0.125(x 4)
Graph each equation.
10. y ⫺ 2 ⫽ x ⫺ 1
2
11. y ⫹ 3 ⫽ 2(x ⫺ 1)
12. y ⫹ 3 ⫽ 3 (x ⫺ 3)
y
y
y
4
x
2
2
2
x
x
2
0
2
4
2
0
2
4
6
2
0
2
4
6
2
4
2
Lesson 5-4, pages 126–127.
Chapter 5
117
For More Practice Go To:
Write an equation in point-slope form of a line that passes through
the given points.
68
2 1
m 4 2 6 3
y y1 m(x – x1)
Let (2, 8) (x1, y1)
1
y 8 3 (x 2)
16. (4, ⫺6) and (5, ⫺4)
4 (6) 2
m
2
1
54
Let (4, 6) (x1, y1)
y 6 2(x 4)
19. (5.2, 1.9) and (⫺3.8, ⫺5.1)
5.1 1.9 7
m
3.8 5.2 9
Let (5.2, 1.9) (x1, y1)
7
y 1.9 (x 5.2)
9
14. (5, 11) and (⫺6, 3)
15. (⫺3, 7) and (4, 14)
8
3 11
6 5 11
Let (5, 11) (x1, y1)
8
y 11 (x 5)
11
m
7
14 7
1
4 (3) 7
Let (3, 7) (x1, y1)
y 7 1(x 3)
m
17. (6, 2) and (8, ⫺5)
18. (⫺12, ⫺9) and (13, ⫺10)
7
5 2
2
86
Let (6, 2) (x1, y1)
7
y 2 (x 6)
2
1
10 (9)
25
13 (12)
Let (12, 9) (x1, y1)
1
y 9 (x 12)
25
m
1
2
1
m
1
20. (3 2 , 2 3 ) and (6 2 , ⫺1 3 )
1 1 2 2
3 4 4
3
m
3
3
6 13 1
2
2
1 2
Let 3 , 2 (x1, y1)
2 3
4
1
2
y2 x3
3
2
3
(
)
(
)
22. Health Insurance Shari’s health insurance plan requires that
she pay a monthly fee and also pay for each visit (her co-pay).
In April, May, and June, Shari went to the doctor’s office
several times. She recorded the number of times and the amount
she paid for health insurance in the table at the right.
1
3
(
Month
April
May
June
Let y1 94.75, m 20.5, x1 2, and x 7; y 94.75 20.5(7 2); y 94.75 102.5
y 197.25. Health insurance will cost Shari $197.25 in July.
Multiply.
23. ⫺95 • 32 (5 100) • 32 5 • 32 100 • 32 160 3200 3040
1
1
1
1
1 2 7 8 2 • 7 2 • 8 14 4 14 4
24. 2 • 7 8
(
)
25. 19.9 • 4.5 (20 0.1) • 4.5 20 • 4.5 0.1 • 4.5 90 0.45 89.55
118
Chapter 5
)
(
115.25 135.75 20.5
20.5; Her co-pay is $20.50 per visit.
1
34
b. If Shari goes to the doctor 7 times in July, how much will she
pay for health insurance?
3
83 63
2
4
4
m
7
24 4 1
5
5
1 3
Let 4 , 6 (x1, y1)
5 4
2
1
3
y6 x4
7
5
4
a. What is her co-pay?
m
4
21. (4 5 , 6 4 ) and (⫺2 5 , 8 4 )
Visits
4
2
3
)
Cost
$135.75
$94.75
$115.25
Copyright © by William H. Sadlier, Inc. All rights reserved.
13. (2, 8) and (⫺4, 6)