Download 5-5 Change the Form of a Linear Equation

5-5 Change the Form of a Linear Equation
Name
Date
Rewrite the linear equation in the indicated form. Then find the value of y
if (2, y) lies on the line.
7x 3y 21; slope-intercept form
7x 7x 3y 21 7x
7x 3y 21
7(2) 3y 21
Substitute 2 for x.
14 3y 21
Simplify.
14 14 3y 21 14
Subtract 14
Subtract 7x
from both sides.
3y 21 7x
3y 21 7x
3
3
from both sides.
Divide both sides
by 3.
3y 7
3y 7
3
3
7
y 7 3x
or
Divide both sides by 3.
7
y3
7
y 3x 7
7
The point (2, 3 ) lies on the line 7x 3y 21.
Find the x- and y-intercepts of each equation. Then draw its graph
on a separate sheet of paper. Check students’ graphs.
1. 8x 5y 40
8(0) 5y 40 8x 5(0) 40
y 8
x5
x-intercept: 5; y-intercept: 8
2. 2x 5y 3.8
2x 5(0) 3.8 2(0) 5y 3.8
x 1.9
y 0.76
x-intercept: 1.9; y-intercept: 0.76
3. 1 2x 3y
1 2(0) 3y 1 2x 3(0)
1
1
x
y
3
2
1
1
x-intercept: ; y-intercept: 2
3
Tell whether the graph is a horizontal or vertical line.
Copyright © by William H. Sadlier, Inc. All rights reserved.
4. 2x 12
x6
x 1 0y 6, so no y-intercept
x-intercept is 6.
vertical line
5. 6x 18
x 3
x 1 0y 5 23, so no y-intercept
x-intercept is 3.
vertical line
6. 1.2y 6
y5
0x 1 y 5 5, no x-intercept
horizontal line
Write each equation in the indicated form.
7. 8x 2y 15
slope-intercept form
8x 8x 2y 8x 15
2y 8x 15
2y
8x 15
2
2
y 4x 7.5
4
10. y 3 5 (x 4)
standard form
5y 15 4x 16
4x 5y 1
8. 9x 3y 7
slope-intercept form
3y 9x 7
7
y 3x 3
11. y 5.6 2(x 4.7)
standard form
y 5.6 2x 9.4
2x y 15
Lesson 5-5, pages 128–131.
3
9. y 2 4 (x 3)
standard form
4y 8 3x 9
3x 4y 1
12. y 7.9 3(x 1.7)
standard form
y 7.9 3x 5.1
3x y 13
Chapter 5
119
For More Practice Go To:
Tell if the given point is on the given line.
13. (3.5, 4.7); 5x 2y 27
14. (4.1, 5.2); 3x 5y 38
?
?
5(3.5) 2(4.7) 27
?
17.5 9.4 27
26.9 27 False; No
16. (6.4, 1.3); y 3x 17.9
3(4.1) 5(5.2) 38
?
12.3 26 38
38.3 38 False; No
2 1
2
17. ( 3 , 4 ); y 2 3 (x 1)
? 2 2
1
2 1
4
3 3
7 ? 2 1
•
4
3 3
7
2
False; No
4
9
(
?
1.3 3(6.4) 17.9
?
1.3 19.2 17.9
1.3 1.3 True; Yes
)
Find the value of x or y so that the given point lies on the given line.
19. (2.4, y); y 3x 1
20. (9.2, y); y 2x 3
y 3(2.4) 1
y 7.2 1
y 6.2
7
22. (x, 8 ); 3x 5y 4
35
3
3x 4; 3x 8
8
1
x
8
?
4.5 2(1.5) 1.5
?
4.5 3 1.5
4.5 4.5 True; Yes
1 3
3
23. (x, 3 ); y 2 4 (x 1)
5
3
3
2 x ; 20 24 9x 9
3
4
4
13 9x
13
x
9
1
18. ( 2 , 8 ); y 1 4 (x 2)
3
1
8
5
8
5
8
1 1
2
4 2
? 1 3
•
4 2
3
False; No
8
?
(
)
2
21. (x, 3 ); 2x 4y 2
2x y 2(–9.2) 3
y 18.4 3
y 15.4
5
15. (1.5, 4.5); y 2x 1.5
8
2
2; 2x 3
3
1
x
3
5
2
24. (x, 6 ); y 3 3 (x 2)
5
2
4
3 x ; 5 18 4x 8
6
3
3
–21 4x
21
x
4
Solve.
Assign numbers to the months involved:
May 2007 0, May 2008 12,
December 2008 19. Ordered pairs are:
(0, 61), (12, 126), (19, y), where y cost of crude
oil in December 2008.
126 61
m
5.416 艐 5.42
12 0
y 126 5.42(19 12); y 126 37.94
y 163.94; y 163.94 fi 200.
Following this trend, the price per barrel of crude
oil will not reach $200 by December 2008.
6.844 5.893 0.951
0.23775
4
2006 2002
Let y1 6.844, m 0.23775, x1 2006, x 2011.
y 6.844 0.23775(2011 2006)
y 6.844 1.18875; y 8.03275 艐 8.033
Following this trend, the U.S. will consume 8.033
quadrillion BTUs of renewable energy in 2011.
m
17
5
27. If the y-intercept of a line is 3 and the slope is 3 , what is the x-intercept?
17
5
17
17 17 5
17
5
x; 17 5x;
y mx b; y x ; 0 x ;
x; The x-intercept is .
5
3
3
3
3 3
5
3
120
Chapter 5
Copyright © by William H. Sadlier, Inc. All rights reserved.
26. Oil Prices In May 2007, the price of crude
oil was at $61 per barrel. A year later, it was
at $126 per barrel. If the price of crude oil
continues to climb at this rate, will 1 barrel cost
more than $200 in December 2008?
25. U.S. Energy Consumption The amount of
renewable energy consumed increased from
5.893 quadrillion BTUs in 2002 to 6.844
quadrillion BTUs in 2006. Based on this data,
what do you predict will be the amount of
renewable energy consumed in 2011. Round
each decimal to the nearest thousandth.