Evaluate:
14)
2x + 7y = −4; (2, −5)
Solution:
put x=2 and y=-5 in the given equation, we get
2*2+7*-5=-4
=> 4-35=-4
=> -31=-4
Given, pair is not solution of given equation.
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16)
−3x − 2y = −15; (7, −3)
Solution:
put x=7 and y=-3 in the given equation, we get
-3*7-2*-3=-15
=> -21+6=-15
=> -15=-15
Given, pair is solution of given equation.
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19)
y = −7; (9, −7)
Solution:
put x=9 and y=-7 in the given equation, we get
-7=-7
Given pair is the solution of given equation.
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*** Complete the ordered pair for each equation.
22) y = −2x + 3; (6, )
On putting x=6 in the given equation, we get
y=-2*6+3=-12+3=-9
Therefore, ordered pair is (6, -9)
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24)
−x + 10y = 8; ( , 2/3 )
On putting y=2/3 in the given equation, we get
-x+10*(2/3)=8
=> -x=8-20/3
=> -x=4/3
=>x= -4/3
Therefore, ordered pair is (-4/3, 2/3)
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28) y = −5x + 1
x
y
0
1
1
-4
2
-9
−1
6
32). 2x − y = 12
x
y
6
0
0
-12
7
−2
-7
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Plot ordered pairs on the graph.
43) (−2, −3)
44) (4, −5)
45) (−5, 0)
8. −x + 5y = 10
x
y
0
2
-10
0
10
4
−3
7/5
39). The cost of downloading popular songs from iTunes is given by y = 1.29x, where x
represents the number of songs downloaded and y represents the cost, in dollars.
a. Make a table of values using x = 0, 4, 7, and 12, and write the information as ordered
pairs.
b. Explain the meaning of each ordered pair in the context of the problem.
c. Graph the equation. Use an appropriate scale.
d. How many songs could you download for $11.61?
solution:
a)
x
y=1.29x
Ordered pair
0
1.29*0=0
(0,0)
4
1.29*4=5.16
(4,5.16)
7
1.29*7=9.03
(7,9.03)
12
1.29*12=15.48
(12,15.48)
b) (0,0) represents if no song is downloaded, there is no cost.
(4,5.16) represents cost of downloading 4 songs from iTunes is $5.16
(7, 9.03) represents cost of downloading 7 songs from iTunes is $9.03
(12,15.48) represents cost of downloading 12 songs from iTunes is $15.48
c)
d) here, we have to find x, when y=11.61
=> 11.61=1.29x
=>x=11.61/1.29=9
9 songs.
.....................................................................
Use the slope formula to find the slope of the line containing each pair of points.
22) (0, 3) and (9, 6)
slope=(6-3)/(9-0)=3/9=1/3
28).
(2, 0) and (−5, 4)
slope=(4-0)/(-5-2)=-4/7
32.(1, 3) and (1, −1)
slope=(-1-3)/(1-1)= not defined.
.................................................................
47 Graph the line containing the given point and with the given slope.
(2, 1) m = ¾
Solution: Equation is given by (y-y1)=m(x-x1)
=> y-1=3/4(x-2)
=>y=(3/4)x-1/2
Use the slope and one point on a line graph the line.
48) ( 1 , 2 ) m = 1/3
Solution: Equation is given by (y-y1)=m(x-x1)
=> y-2=(1/3)(x-1)
=>y=(1/3)x+(5/3)
58) (−1, −2); m = 0
Solution: Equation is given by (y-y1)=m(x-x1)
=> y+2=0(x+1)
=>y=-2
60) (2, 0); slope is undefined.
Solution: Equation is given by (y-y1)=m(x-x1)
1/m=0
=> 0(y-0)=(x-2)
=> x=2
Each of the following equations is in slope-intercept form. Identify the slope and the y-intercept,
then graph each line using this information.
solution: On comparing it with y=mx+b, we get
slope m=7/5
intercept b= -1
Solution: On comparing it with y=mx+b, we get
slope m=2/3
intercept b= 5
Put each equation into slope-intercept form, if possible, and graph.
18). x + 2y = −8
=> 2y= -x-8
=>y= (-1/2)x-4
20) 2x − 5y = 5
=> 5y=2x-5
=> y=(2/5)x-1
Write the slope-intercept form for the equation of a line with the given slope and yintercept.
33) m = −4; y-int: (0, 7)
solution: Equation of line is given by y=mx+b
=> y= -4x+7
34) m = −7; y-int: (0, 4)
solution: Equation of line is given by y=mx+b
=> y= -7x+4
Determine whether each pair of lines is parallel, perpendicular, or neither.
50)
Solution. Slope of first line is 3/4 and again slope of second line is 3/4
since both slopes are same. Lines are parallel.
52)
slope of first line is 4/5.
slope of second line is -4/5
Both are not equal and not negative reciprocal of each other. Hence, neither parallel not
perpendicular.
62)
Slope of both lines is 0. Hence lines are parallel.