Name: 
 

Algebra 1 Chapter 6


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 
 
The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.
 

 1. 

Time (days)
Cost ($)
3
75
4
100
5
125
6
150
a.
mc001-1.jpg dollars per day; the cost is $25 for each day.
b.
mc001-2.jpg dollars per day; the cost is $25 for each day.
c.
mc001-3.jpg dollars per day; the cost is $75 for each day.
d.
mc001-4.jpg dollars per day; the costs $1 for 150 days
 

 2. 

Time (hours)
Distance (miles)
4
260
6
390
8
520
10
650
a.
10; Your car travels for 10 hours.
b.
260; Your car travels 260 miles.
c.
mc002-1.jpg; Your car travels 65 miles every 1 hour.
d.
mc002-2.jpg; Your car travels 65 miles every 1 hour.
 
 
The rate of change is constant in the graph. Find the rate of change. Explain what the rate of change means for the situation.
 

 3. 
mc003-1.jpg
a.
–100; value drops $100 every year.
b.
mc003-2.jpg; value drops $100 every 3 years.
c.
–3; value drops $3 every year.
d.
–1; value drops $1 every year.
 

 4. 
mc004-1.jpg
a.
mc004-2.jpg; the balloon rises mc004-3.jpg ft every second.
b.
2000; every 2000 seconds the balloon rises 1 ft.
c.
mc004-4.jpg; the balloon rises mc004-5.jpg ft every second.
d.
30; every 30 seconds the balloon rises 0.5 ft.
 
 
Find the rate of change for the situation.
 

 5. 
You run 7 miles in one hour and 21 miles in three hours.
a.
3 miles per hour
c.
7 miles
b.
3 hours
d.
7 miles per hour
 

 6. 
A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.
a.
mc006-1.jpg lb per person
c.
mc006-2.jpg lb per person
b.
4 lb per person
d.
36 people
 
 
Find the slope of the line.
 

 7. 
mc007-1.jpg
a.
 mc007-2.jpg
b.
mc007-3.jpg
c.
 mc007-4.jpg
d.
mc007-5.jpg
 

 8. 
mc008-1.jpg
a.
 – mc008-2.jpg
b.
 mc008-3.jpg
c.
 mc008-4.jpg
d.
mc008-5.jpg
 
 
Find the slope of the line that passes through the pair of points.
 

 9. 
(1, 7), (10, 1)
a.
mc009-1.jpg
b.
mc009-2.jpg
c.
mc009-3.jpg
d.
mc009-4.jpg
 

 10. 
(–5.5, 6.1), (–2.5, 3.1)
a.
–1
b.
mc010-1.jpg
c.
–1
d.
1
 

 11. 
A student finds the slope of the line between (14, 1) and (18, 17). She writes mc011-1.jpg. What mistake did she make?
a.
She should have added the values, not subtracted them.
b.
She used y-values where she should have used x-values.
c.
She mixed up the x- and y-values.
d.
She did not keep the order of the points the same in numerator and the denominator.
 
 
State whether the slope is 0 or undefined.
 

 12. 
mc012-1.jpg
a.
undefined
b.
0
 

 13. 
mc013-1.jpg
a.
0
b.
undefined
 

 14. 
mc014-1.jpg
Use the graph.
a. Which plant was the tallest at the beginning?
b. Which plant had the greatest rate of change over the 6 weeks?
a.
plant 2; plant 2
c.
plant 3; plant 1
b.
plant 1; plant 3
d.
plant 3; plant 3
 
 
Find the slope and y-intercept of the line.
 

 15. 
y = mc015-1.jpgx – 3
a.
3; mc015-2.jpg
b.
–3;mc015-3.jpg
c.
mc015-4.jpg; 3
d.
mc015-5.jpg; –3
 

 16. 
14x + 4y = 24
a.
mc016-1.jpg; mc016-2.jpg
c.
mc016-5.jpg; mc016-6.jpg
b.
mc016-3.jpg; mc016-4.jpg
d.
mc016-7.jpg; mc016-8.jpg
 
 
Write an equation of a line with the given slope and y-intercept.
 

 17. 
m = 1, b = 4
a.
y = 4x + 1
c.
y = –1x + 4
b.
y = x – 4
d.
y = x + 4
 

 18. 
m = mc018-1.jpg, b = mc018-2.jpg
a.
y = mc018-3.jpgx – mc018-4.jpg
c.
y = mc018-7.jpgx + mc018-8.jpg
b.
y = mc018-5.jpgx – mc018-6.jpg
d.
y = mc018-9.jpgx + mc018-10.jpg
 
 
Write the slope-intercept form of the equation for the line.
 

 19. 
mc019-1.jpg
a.
y = mc019-2.jpgx mc019-3.jpg1
c.
y = mc019-6.jpgx mc019-7.jpg1
b.
y = mc019-4.jpgx mc019-5.jpg1
d.
y = mc019-8.jpgx mc019-9.jpg1
 

 20. 
mc020-1.jpg
a.
y = mc020-2.jpgx mc020-3.jpg
c.
y = mc020-6.jpgx mc020-7.jpg
b.
y = mc020-4.jpgx mc020-5.jpg
d.
y = mc020-8.jpgx + mc020-9.jpg
 

 21. 
Use the slope and y-intercept to graph the equation.
y = mc021-1.jpgx – 3
a.
mc021-2.jpg
c.
mc021-4.jpg
b.
mc021-3.jpg
d.
mc021-5.jpg
 

 22. 
Giselle pays $210 in advance on her account at the athletic club. Each time she uses the club, $10 is deducted from the account. The situation can be modeled by the equation
b = 210 – 10x, where x is the number of visits and b is the total account balance.

a. Graph the equation.
b. Find the account balance after 8 visits.
a.
mc022-1.jpg
$140
c.
mc022-3.jpg
$290
b.
mc022-2.jpg
$130
d.
mc022-4.jpg
$110
 
 
Find the x- and y-intercept of the line.
 

 23. 
2x + 3y = –18
a.
x-intercept is 18; y-intercept is 18.
c.
x-intercept is 2; y-intercept is 3.
b.
x-intercept is –6; y-intercept is –9.
d.
x-intercept is –9; y-intercept is –6.
 

 24. 
–3x + 9y = 18
a.
x-intercept is 2; y-intercept is –6.
c.
x-intercept is –6; y-intercept is 2.
b.
x-intercept is –3; y-intercept is 9.
d.
x-intercept is 9; y-intercept is –3.
 
 
Match the equation with its graph.
 

 25. 
–7x + 7y = –49
a.
mc025-1.jpg
c.
mc025-3.jpg
b.
mc025-2.jpg
d.
mc025-4.jpg
 

 26. 
Write y = mc026-1.jpgx + 7 in standard form using integers.
a.
–2x + 3y = 21
c.
–2x – 3y = 21
b.
3x – 2y = 21
d.
–2x + 3y = 7
 

 27. 
The grocery store sells kumquats for $4.25 a pound and Asian pears for $2.25 a pound. Write an equation in standard form for the weights of kumquats k and Asian pears p that a customer could buy with $18.
a.
4.25k + 2.25p = 18
c.
4.25k = 2.25p + 18
b.
4.25p + 2.25k = 18
d.
4.25 + 2.25 = k
 

 28. 
Write an equation of a line that has the same slope as 2x – 5y = 12 and the same y-intercept as 4y + 24 = 5x.
a.
mc028-1.jpg
c.
mc028-3.jpg
b.
mc028-2.jpg
d.
mc028-4.jpg
 
 
Graph the equation.
 

 29. 
y + 2 = –(x – 4)
a.
mc029-1.jpg
c.
mc029-3.jpg
b.
mc029-2.jpg
d.
mc029-4.jpg
 

 30. 
y + 5 = mc030-1.jpg(x + 2)
a.
mc030-2.jpg
c.
mc030-4.jpg
b.
mc030-3.jpg
d.
mc030-5.jpg
 

 31. 
y = –3
a.
mc031-1.jpg
c.
mc031-3.jpg
b.
mc031-2.jpg
d.
mc031-4.jpg
 

 32. 
x = –4
a.
mc032-1.jpg
c.
mc032-3.jpg
b.
mc032-2.jpg
d.
mc032-4.jpg
 
 
Write an equation in point-slope form for the line through the given point with the given slope.
 

 33. 
(4, –6); m = mc033-1.jpg
a.
mc033-2.jpg
c.
mc033-4.jpg
b.
mc033-3.jpg
d.
mc033-5.jpg
 

 34. 
(10, –9); m = mc034-1.jpg
a.
y – 10 = mc034-2.jpg(x + 9)
c.
y – 9 = mc034-4.jpg(x – 10)
b.
y – 9 = mc034-3.jpg(x + 10)
d.
y + 9 = mc034-5.jpg(x – 10)
 

 35. 
A line passes through (1, –5) and (–3, 7).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in slope-intercept form.
a.
y – 5 = 3(x + 1); y = 3x + 8
c.
mc035-2.jpg
b.
mc035-1.jpg;
d.
y + 5 = –3(x – 1); y = –3x – 2
 

 36. 
A line passes through (2, –1) and (8, 4).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in standard form using integers.
a.
 y + 1 = mc036-1.jpg(x – 2); –5x + 6y = –16
c.
 y + 1 = mc036-3.jpg(x + 2); –5x + 6y = –16
b.
 y – 1 = mc036-2.jpg(x – 2); –5x + 6y = 16
d.
 y – 2 = mc036-4.jpg(x + 1); –5x + 6y = 17
 
 
Is the relationship shown by the data linear? If so, model the data with an equation.
 

 37. 

x
y
–9
–2
–5
–7
–1
–12
3
–17
a.
The relationship is linear; y + 2 = mc037-1.jpg(x + 9).
b.
The relationship is linear; y + 9 = mc037-2.jpg(x + 2).
c.
The relationship is not linear.
d.
The relationship is linear; y + 2 = mc037-3.jpg(x + 9).
 

 38. 

x
y
3
1
7
2
11
3
18
5
a.
The relationship is not linear.
b.
The relationship is linear; mc038-1.jpg.
c.
The relationship is linear; mc038-2.jpg.
d.
The relationship is linear; mc038-3.jpg.
 

 39. 
In February, you have a balance of $270 in your bank account. Each month you deposit $45. Let January = 1, February = 2, and so on. Write an equation for this situation. Use the equation to find the balance in June.
a.
y – 270 = 45(x – 2) ; $450
c.
y = 45(x – 4); $180
b.
y = 45(x – 4); $270
d.
y – 270 = 45x; $45
 

 40. 
The table shows the height of a plant as it grows.
a. Model the data with an equation.
b. Based on your model, predict the height of the plant at 12 months.

Time (months)
Plant Height (cm)
3
9
5
15
7
21
9
27
a.
 y – 3 = mc040-1.jpg(x –9); 39 cm
c.
y – 9 = mc040-2.jpg(x –3); 18 cm
b.
y – 9 = 3(x –3); 36 cm
d.
 The relationship cannot be modeled.
 
 
Are the graphs of the lines in the pair parallel? Explain.
 

 41. 
y = mc041-1.jpgx + 8
–2x + 12y = –11
a.
Yes, since the slope are the same and the y-intercepts are the same.
b.
No, since the y-intercepts are different.
c.
Yes, since the slope are the same and the y-intercepts are different.
d.
No, since the slopes are different.
 

 42. 
y = 5x + 6
–18x + 3y = –54
a.
No, since the slopes are different.
b.
Yes, since the slopes are the same and the y-intercepts are different.
c.
No, since the y-intercepts are different.
d.
Yes, since the slope are the same and the y-intercepts are the same.
 

 43. 
The map shows Hope Road and the construction site for the new library. Find the equation of a “street”that passes through the building site and is parallel to Hope Road.
mc043-1.jpg
a.
y = mc043-2.jpgx + 4
c.
y = mc043-4.jpgx + 4
b.
y = mc043-3.jpgx – 4
d.
y = mc043-5.jpgx + 4
 
 
Write an equation for the line that is parallel to the given line and that passes through the given point.
 

 44. 
y = –5x + 3; (–6, 3)
a.
y = –5x + 27
c.
y = 5x – 9
b.
y = –5x – 27
d.
y = –5x + 9
 

 45. 
y = mc045-1.jpgx – 9; (–8, –18)
a.
y = mc045-2.jpgx mc045-3.jpg
c.
y = mc045-5.jpgx – 12
b.
y = mc045-4.jpgx – 12
d.
y = mc045-6.jpgx + 12
 
 
Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
 

 46. 
7x – 4y = 4
x – 4y = 3
a.
perpendicular
b.
parallel
c.
neither
 

 47. 
y = mc047-1.jpgx – 11
16x – 8y = –8
a.
neither
b.
perpendicular
c.
parallel
 
 
Write the equation of a line that is perpendicular to the given line and that passes through the given point.
 

 48. 
4x – 12y = 2; (10, –1)
a.
y = mc048-1.jpgx + 29
c.
y = mc048-3.jpgx + 29
b.
y = mc048-2.jpgx + 29
d.
y = mc048-4.jpgx + 7
 

 49. 
mc049-1.jpg; (–6, 5)
a.
mc049-2.jpg
c.
mc049-4.jpg
b.
mc049-3.jpg
d.
mc049-5.jpg
 

 50. 
Assume that the two lines are perpendicular.
mc050-1.jpg
a. Find a slope-intercept equation for line A.
b. Find a point-slope equation for line B.

a.
mc050-2.jpg
c.
mc050-4.jpg
b.
mc050-3.jpg
d.
mc050-5.jpg
 

 51. 
Which graph shows the best trend line for the following data.
mc051-1.jpg
a.
mc051-2.jpg
c.
mc051-4.jpg
b.
mc051-3.jpg
d.
mc051-5.jpg
 
 
Use a graphing calculator to find the equation of the line of best fit for the data. Find the value of the correlation coefficient r.
 

 52. 

Average Speed (mi/h)
Time (hours)
8.5
2.5
7.5
3.75
6.5
4.5
6.0
5.0
5.5
5.5
5.0
6.25
4.0
6.75
3.5
8.75
a.
y = 11.83x – 1. 11; r = –0.9760964904
b.
y = –1.11x + 11.83; r = –0.9760964904
c.
y = 11.83x – 1. 11; r = 0.9527643586
d.
y = –1.11x + 11.83; r = 0.9527643586
 

 53. 
Christine’s Best Javelin Throws
mc053-1.jpg
(Use x = 0 for 1997.)
a.
y = 31.15x + 0.864; r = 0.7139281244
b.
y = –0.864x + 31.15; r = 0.7139281244
c.
y = 31.15x + 0.864; r = 0.8449426752
d.
y = 0.864x + 31.15; r = 0.8449426752
 

 54. 
The table shows the amount of time a student spends practicing each week and her typing speed.

mc054-1.jpg

a. Use a graphing calculator to find the equation of the line of best fit.
b. Use your equation to predict the student’s typing speed if she spends 8 hours practicing each week.
a.
y = 5.1 x + 17; about 47 words per minute
b.
y = 17.1x + 4.9; about 142 words per minute
c.
y = 4.9x + 17.1; about 56 words per minute
d.
y = 4.6x + 16; about 53 words per minute
 

 55. 
Describe how the graph is like the graph of y = | x | and how it is different.
mc055-1.jpg
a.
The graphs have the same y-intercept. The second graph is steeper than y = | x |.
b.
The graph is the same as y = | x |.
c.
The graphs are the same shape. The y-intercept of y = | x | is 0 and the x-intercept of the second graph is –4.
d.
The graphs are the same shape. The y-intercept of y = | x | is 0 and the y-intercept of the second graph is –4.
 

 56. 
Graph y = | x | – 5.
a.
mc056-1.jpg
c.
mc056-3.jpg
b.
mc056-2.jpg
d.
mc056-4.jpg
 
 
Write an equation for each translation of nar020-1.jpg.
 

 57. 
2 units up
a.
y = | x | – 2
c.
y = | 2x |
b.
y + 2 = | x |
d.
y = | x | + 2
 

 58. 
4.5 units up
a.
y = | x | + 4.5
c.
y = | 4.5x |
b.
y = | x | – 4.5
d.
y + 4.5 = | x |
 

 59. 
6 units left
a.
y = | x + 6 |
b.
y = | x – 6 |
c.
y = | x | + 6
d.
y = | x | – 6
 

 60. 
16.5 units right
a.
y = | x – 16.5 |
b.
y = | x | + 16.5
c.
y = | x | – 16.5
d.
y = | x + 16.5 |
 
 
Graph each equation by translating y = | x |.
 

 61. 
y = | x + 6 |
a.
mc061-1.jpg
c.
mc061-3.jpg
b.
mc061-2.jpg
d.
mc061-4.jpg
 

 62. 
y = | x + 2 |
a.
mc062-1.jpg
c.
mc062-3.jpg
b.
mc062-2.jpg
d.
mc062-4.jpg
 

 63. 
y = | x – 3 | – 4
a.
mc063-1.jpg
c.
mc063-3.jpg
b.
mc063-2.jpg
d.
mc063-4.jpg
 

 64. 
mc064-1.jpg
Bella wants to write two equations to model the streets on this map. She can use y = x – 4 to describe Platte Way. Find one absolute value equation to describe Marteen Rd and Smith St.
a.
y = | x – 2 | – 3
c.
y = | x + 3 | – 2
b.
y = | x + 2 | – 3
d.
y = | x – 3 | – 2
 

Short Answer
 

 65. 
Suppose you have $20.00 to buy cold cuts for a class picnic. Ham costs $3.99 per pound and turkey costs $4.99 per pound. The equation 3.99x + 4.99y = 20 models this situation. What does the x-intercept of the graph of the equation tell you about the amount of meat you can buy?
 

 66. 
Gloria makes and sells handmade greeting cards. The scatter plot shows the number of cards she made over a 10-hour period. Find the equation of a trend line and use it to predict the number of cards Gloria can make in 12 hours.

sa066-1.jpg
 

 67. 
The population of a small town is shown in the table.

sa067-1.jpg

Would you expect the correlation coefficient for the line of best fit to be positive or negative? Explain your answer.
 

 68. 
Translate sa068-1.jpg to graph sa068-2.jpg + 2
 

Essay
 

 69. 
Write y = es069-1.jpgx – 11 in standard form. Show your work. Justify each step.
 

 70. 
Use the map to answer the following. Show your work.

es070-1.jpg

a. What is the slope of the line representing Elm Street?
b. Show that Birch Street and Poplar Avenue are parallel.
c. Show that Fir Street is NOT perpendicular to Birch Street.
 

 71. 
The table shows the time spent researching the stock market each week and the average weekly percent gain for an investor over one year.

es071-1.jpg

a. Graph the data.
b. Find an equation for the trend line of the data.
c. Estimate the average weekly percent gain from researching the stock market for 20 hours per week.
 

Other
 

 72. 
The table shows how much a carpenter charges for work. Is the relationship shown by the data in the table linear? Explain your answer.

Hours Worked
Amount Charged ($)
1
25
2
40
3
60
4
80
 

 73. 
Tell whether the following statement is true or false. If false, give a counterexample. Justify your answer:

A rate of change must be negative or zero.
 

 74. 
Why is it NOT possible to write the equation of the line through (–8, –5) and (–8, –9) in slope-intercept form?
 



 
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