Question : Choose the one alternative that best completes the statement : 2152283
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find a point-slope form for the equation of the line satisfying the conditions.
61) y = 17(x + 3) - 4
A) x-intercept is - (47/17); y-intercept is 47
B) x-intercept is (47/17); y-intercept is 47
C) x-intercept is 47; y-intercept is 55
D) x-intercept is - (55/17); y-intercept is -47
62) y = -7(x - 1) - 1
A) x-intercept is - (6/7); y-intercept is -6
B) x-intercept is (8/7); y-intercept is 6
C) x-intercept is (6/7); y-intercept is 8
D) x-intercept is (6/7); y-intercept is 6
63) y = -11(x - 1) + 2
A) x-intercept is - (9/11); y-intercept is 13
B) x-intercept is (13/11); y-intercept is 13
C) x-intercept is - (13/11); y-intercept is -13
D) x-intercept is (9/11); y-intercept is 9
64) y = 13(x + 4) + 1
A) x-intercept is - (53/13); y-intercept is 53
B) x-intercept is (53/13); y-intercept is 51
C) x-intercept is - (53/13); y-intercept is -53
D) x-intercept is (53/13); y-intercept is -53
The table lists data that are exactly linear. (i) Find the slope-intercept form of the line that passes through these data points. (ii) Predict y when x = -1.5 and 4.6.
65)
A) y = -2.4x - 9; y = -5.4, y = -20.04
B) y = -2.4x + 9; y = 12.6, y = -2.04
C) y = 2.4x - 9; y = -12.6, y = 2.04
D) y = 2.4x + 9; y = 5.40, y = 20.04
66) 
A) y = 0.7x - 4.9; y = -5.95, y = -1.68
B) y = -0.7x + 4.9; y = 5.95, y = 1.68
C) y = 0.7x + 4.9; y = 3.85, y = 8.12
D) y = -0.7x - 4.9; y = -3.85, y = -8.12
67) 
A) y = -0.9x + 9.9; y = 11.25, y = 5.76
B) y = -9.9x + 9.9; y = 4.95, y = 55.44
C) y = -0.9x + 9; y = 7.65, y = 13.14
D) y = 0.9x + 9.9; y = 8.55, y = 14.04
68) 
A) y = 3.2x - 4; y = -8.8, y = 10.72
B) y = 3.2x - 7.2; y = -12, y = 7.52
C) y = 3.2x + 5.6; y = 0.8, y = 20.32
D) y = 3.2x + 2.4; y = -2.4, y = 17.12
69) 
A) y = 2.8x + 9.5; y = 5.3, y = 22.38
B) y = 2.8x - 1.7; y = -5.9, y = 11.18
C) y = 2.8x - 9.5; y = -13.7, y = 3.38
D) y = -2.8x + 9.5; y = 13.7, y = -3.38
70)
A) y = -4.6x + 93.3; y = 100.2, y = 72.14
B) y = 2.3x + 93.3; y = 89.85, y = 103.88
C) y = 4.6x + 93.3; y = -100.2, y = -72.14
D) y = -2.3x + 93.3; y = 96.75, y = 82.72
71)
A) y = 6.4x + 13.6; y = 4, y = 43.04
B) y = 3.4x + 13.6; y = 8.5, y = 29.24
C) y = 2.4x + 13.6; y = 10, y = 24.64
D) y = -3.4x - 13.6; y = -8.5, y = -29.24
72)
A) y = 10.9x + 40.8; y = 24.45, y = 90.94
B) y = 4.9x + 40.8; y = 33.45, y = 63.34
C) y = 8.9x + 40.8; y = 27.45, y = 81.74
D) y = -8.9x - 40.8; y = -27.45, y = -81.74
Solve the problem.
73)
Abbey is driving a delivery truck on a straight road. The graph shows the distance y in kilometers that Abbey is from Store A after x hours. (i) Is Abbey traveling toward or away from Store A? (ii) Find the slope of the line.
A) Away; slope is 80.
B) Toward; slope is -40.
C) Away; slope is 20.
D) Toward; slope is -20.
74)
Abbey is driving a delivery truck on a straight road. The graph shows the distance y in kilometers that Abbey is from Store A after x hours. (i) Find the slope-intercept form of the equation of the line. (ii) Use the graph to estimate the y-coordinate of the point (6, y) that lies on the line.
A) y = 25x + 300; (6, 450)
B) y = 25x - 300; (6, -150)
C) y = -50x + 300; (6, 0)
D) y = -25x + 300; (6, 150)
75)
The graph shows the amount of water in a 450-gallon tank after x minutes have elapsed. (i) Is the water entering or leaving the tank? (ii) Find the x-intercept and the y-intercept.
A) Leaving; x-intercept is 0 and y-intercept is 450
B) Leaving; both intercepts are 0
C) Entering; x-intercept is 450 and y-intercept is 0
D) Entering; both intercepts are 0
76)
The graph shows the amount of oil in a 150-gallon tank after x minutes have elapsed. (i) Find the slope-intercept form of the equation of the line. (ii) Use the graph to estimate the x-coordinate of the point (x, 30) that lies on the line..
A) y = 15x; (2, 30)
B) y = 15x - 2; (0, 30)
C) y = 15x + 2; (2, 32)
D) y = -15x; (2, -30)
77)
The graph models the average amount spent annually on entertainment per household in Country X from 1981 to 1987. (i) Find the slope of the line. (ii) Find a point-slope form for the line. (Answers may vary.)
A) Slope is 375; point-slope form is y = 375(x - 1982) + 1500.
B) Slope is 525; point-slope form is y = 525(x - 1984) + 2850.
C) Slope is 675; point-slope form is y = 675(x - 1982) + 1500.
D) Slope is 825; point-slope form is y = 825(x - 1984) + 2850.
78) In 1990 the number of factory pollution incidents reported in Country X was 7500. This number had decreased roughly at a rate of 440 per year since 1982. (i) Find an equation of a line y = m(x - h) + k that describes this data, where y represents the number of pollution incidents during the year x. (Answers may vary.) (ii) Estimate the year when there were approximately 8250 incidents.
A) y = -440(x - 1990) + 7500; 1988
B) y = -440(x - 1982) + 7500; 1980
C) y = -440(x - 1988) + 7500; 1986
D) y = -7500(x - 1990) + 440; 1983
79) The cost of owning a home includes both fixed costs and variable utility costs. Assume that it costs $2098 per month for mortgage and insurance payments and it costs an average of $2.87 per unit for natural gas, electricity, and water usage. (i) Determine a linear function that computes the annual cost of owning this home if x utility units are used. (ii) What does the y-intercept on the graph of the function represent?
A) y = 2.87x + 25,176; y-intercept, 25,176, represents the minimum cost of owning the home for 12 months without spending anything on utilities.
B) y = -2.87x + 2098; y-intercept, 2098, represents the minimum cost of owning the home without spending anything on utilities.
C) y = 2.87x + 2098; y-intercept, 2098, represents the minimum cost of owning the home without spending anything on utilities.
D) y = -2.87x + 25,176; y-intercept, 25,176, represents the minimum cost of owning the home for 12 months without spending anything on utilities.
Solve the problem using your calculator.
80) Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs. Use linear regression to find a linear function that predicts a student's current GPA as a function of his or her entering GPA.
Entering GPA Current GPA
3.5 3.6
3.8 3.7
3.6 3.9
3.6 3.6
3.5 3.9
3.9 3.8
4.0 3.7
3.9 3.9
3.5 3.8
3.7 4.0
A) y = 3.67 + 0.0313x
B) y = 5.81 + 0.497x
C) y = 2.51 + 0.329x
D) y = 4.91 + 0.0212x
81) The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Use linear regression to find a linear function that predicts a student's score as a function of the number of hours he or she studied.
A) y = -67.3 + 1.07x
B) y = 33.7 - 2.14x
C) y = 67.3 + 1.07x
D) y = 33.7 +2.14x
82) The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Use linear regression to find a linear function that predicts the number of products sold as a function of the cost of advertising.
A) y = 55.8 + 2.79x
B) y = -26.4 - 1.42x
C) y = 26.4 + 1.42x
D) y = 55.8 - 2.79x
83) The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters). Use linear regression to find a linear function that predicts a plant's growth as a function of temperature.
A) y = 7.30 - 0.112x
B) y = -14.6 - 0.211x
C) y = 14.6 + 0.211x
D) y = 7.30 + 0.122x
84) A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. Use linear regression to find a linear function that predicts a student's course grade as a function of the number of hours spent in lab.
Number of hours spent in lab Grade (percent)
10 96
11 51
16 62
9 58
7 89
15 81
16 46
10 51
A) y = 0.930 + 44.3x
B) y = 88.6 - 1.86x
C) y = 44.3 + 0.930x
D) y = 1.86 + 88.6x
85) Two separate tests are designed to measure a student's ability to solve problems. Several students are randomly selected to take both tests and the results are shown below. Use linear regression to find a linear function that predicts a student's score on Test B as a function of his or her score on Test A.
A) y = 19.4 + 0.930x
B) y = -0.930 + 19.4x
C) y = -19.4 - 0.930x
D) y = 0.930 - 19.4x
Solve the problem.
86) Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs. By using linear regression, the following function is obtained: y = 3.67 + 0.0313x where x is entering GPA and y is current GPA. Use this function to predict current GPA of a student whose entering GPA is 3.8. Round to the nearest hundredth.
Entering GPA Current GPA
3.5 3.6
3.8 3.7
3.6 3.9
3.6 3.6
3.5 3.9
3.9 3.8
4.0 3.7
3.9 3.9
3.5 3.8
3.7 4.0
A) 3.79
B) 3.30
C) 3.59
D) 3.41
87) The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. By using linear regression, the following function is obtained: y = 67.3 + 1.07x where x is number of hours studied and y is score on the test. Use this function to predict the score on the test of a student who studies 11 hours. Round to the nearest tenth.
A) 79.1
B) 74.1
C) 83.8
D) 84.1
88) The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). By using linear regression, the following function is obtained: y = 55.8 + 2.79x where x is the cost of advertising (in thousands of dollars) and y is number of products sold (in thousands). Use this function to predict the number of products sold if the cost of advertising is $7000. Round to the nearest hundredth.
A) 72.33
B) 75.33
C) 82.03
D) 19,585.8
89) The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters). By using linear regression, the following function is obtained: y = 14.6 + 0.211x where x is temperature and y is growth in millimeters. Use this function to predict the growth of a plant if the temperature is 69. Round to the nearest hundredth.
A) 27.71
B) 29.16
C) 29.71
D) 30.26
90) A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. By using linear regression, the following function is obtained: y = 88.6 - 1.86x where x is the number of hours spent in the lab and y is the grade on the test. Use this function to predict the grade of a student who spends 14 hours in the lab. Round to the nearest tenth.
Number of hours spent in lab Grade (percent)
10 96
11 51
16 62
9 58
7 89
15 81
16 46
10 51
A) 62.6
B) 65.4
C) 58.6
D) 74.6
