Deck 3: Thinking Linearly

Question 1

Graph the line by making a table of ordered pairs and plotting the points.
y = 5x - 10

Answer 1

Question 2

Write the linear equation in slope-intercept form.
8x - y = 24

Answer 2

y = 8x - 24

Question 3

Write a variation model. Use k as the constant of variation. the distance (d)traveled by an object varies directly as the average speed (v)

Answer 3

D = KV

Question 4

Which of the following graphs shows the correct location of the points (4,5)and (-2, -4)?

Question 5

Which of the following graphs shows the correct location of the point (-3, 4)?

Question 6

Graph the line by making a table of ordered pairs and plotting the points.
-27y = 14x

Question 7

Graph the line by making a table of ordered pairs and plotting the points.
3x + 2y = -11.

Question 8

Plot each of the following points on the same set of axes.

Question 9

Complete the table of poins for the equation
Then use those points skecth the graph.

Question 10

Which table of points is correct for the equation -y= 36 - 9x?

A)

B)

C)

D)

Question 11

Find the slope and y-intercept, and use them to sketch the graph.
y = -4x + 21

Question 12

Which is the graph of 5x + 2y = 100?

Question 13

Solve the system by graphing.

Question 14

Find the slope and y-intercept, and use them to sketch the graph.
y = -4x + 21

Question 15

Which point is a solution to the system?

Question 16

Plot each of the following points on the same set of axes.

Question 17

Complete the table of points for the equation y = x - 7.

Question 18

Complete the table of points for the equation 8x - 2y = 6. (If answers are decimals, round to one decimal place.)

Question 19

Find the slope and y-intercept of the equation.
y + 12 = -2x

Question 20

Solve the system using the graphing method.

Question 21

x varies directly as p . If x=14 when p=2 , find x when p is 7 .

A) x=1
B) x=14
C) x=49
D) x=343

Question 22

Sketch the graph of 2x = 11.

Question 23

The price per share of stock (in dollars)over a period of 5 days is shown in the
graph. What was the loss between day 3 and day 4?

Question 24

Determine if the given point is a solution to the system.

A)no
B)yes

Question 25

Find the slope and y-intercept of the equation.

Question 26

Find the slope of the line connecting the points (-7,4) and (-7,9) .

A) m=0
B) m=1.5
C) undefined
D) m=5

Question 27

Sketch the graph of the equation.
4x + y = -4

Question 28

Find the slope of the line that passes through the points (8,-6) and (10,-12) .

A) m=-3
B)
C)
D) m=3

Question 29

The price per share of stock (in dollars)over a period of 5 days is shown in the
graph. What was the gain between day 4 and day 5?

Question 30

Graph the line by making a table of ordered pairs and plotting the points.

Question 31

Find the slope of the line that passes through the points (-8, 2)and (-12, 2).

A)m = -4
B)undefined
C)m = 0
D)m = 1.4

Question 32

Find the slope of the line that passes through the points (2.4, 0.2)and (1.6, 1.2)

Question 33

Graph the line by making a table of ordered pairs and plotting the points.

Question 34

Sketch the graph of the equation.

Question 35

Find the slope and y-intercept, and use them to sketch the graph.
y = -4x + 21

Question 36

Find the slope and y-intercept, and use them to sketch the graph.

Question 37

Plot each of the following points on the same set of axes.

Question 38

Find the slope and y-intercept, and use them to sketch the graph.

Question 39

Write an equation of the line with slope and y -intercepp

A)

B)

C)

D)

Question 40

Find the slope and y-intercept, and use them to sketch the graph.

Question 41

Solve the system using the substitution method.

Question 42

Solve the system by graphing.

Question 43

Solve the system using the substitution method.

Question 44

Solve the system using the substitution method.

Question 45

Write a variation model. Use as the constant of variation.
the cost (D) of filling your gas tank is directly proportional to the price (p) per gallon of gas

A)

B)

C)

D)

Question 46

Solve the system using the substitution method.

Question 47

Graph the line through the point (-1, 3) having slope -2.

A)

B)

C)

D)

Question 48

Write an equation of the line with slope and y -intercept

A)

B)

C)

D)

Question 49

Does the line pictured below have positive, negative, zero, or undefined slope?

Question 50

Determine the slope by using the slope formula and any two points on the line.

Question 51

Solve the system using the substitution method.

Question 52

Solve the system using the substitution method.

Question 53

Determine the slope by using the slope formula and any two points on the line.

Question 54

Find the constant of variation, k .
a varies directly as b and a is 27 when b is 36 .

A)
B)
C) k=972
D)

Question 55

Use the graph to determine the solution to the system.

Question 56

Find the slope and y-intercept.

Question 57

Solve the system by graphing.

Question 58

Solve the system using the substitution method.

Question 59

Does the line pictured below have positive, negative, zero, or undefined slope?

Question 60

Determine if the given point is a solution to the system.

Question 61

Of all the topics we have covered in unit 3, what has stood out to you as something most relevant
to your life? Explain why.

Question 62

Mountain climbers use a general rule of thumb which estimates that the temperature will drop 3.5 degrees Fahrenheit for every 1000 ft of elevation.
b. Find the slope of the line and explain what it means.
c. Find the y-intercept and explain what it means.
d. Write the equation of the line.
e. Restate your equation in the form of a sentence: "If x represents …, then y = … represents …"
f. Use your equation to find the temperature at 10,000 ft.

Question 63

B varies directly as m and inversely n . B=36 when m=54 and n=9 , find B when m= 7 and n=5 .

A)

B)

C)

D)

Question 64

The following table reports the number of yellow fever cases reported in Ghana for the years 1992-2004 (after the start of mass immunization). b. What trends do you see? Be specific.

Question 65

Find the slope of the line connecting the points

A)

B)

C)

D)

Question 66

The cost, in dollars, of filling your gas tank is directly proportional to the price per gallon of gas. If 8 gallons of gas costs $10.00, how much would 11 gallons cost?

A)$15.00
B)$11.25
C)$13.75
D)$13.00

Question 67

The table displays the number of women in the US House of Representatives for selected years from 1980 through 2008.
a. Use your calculator to determine the line of best fit for these data, where x is the number of years since 1980. Round all coefficients to 4 decimal places.
b. What is the correlation coefficient, r? What does it mean about whether this line is a good fit for these data? Explain.
c. Give the slope of the line and explain what it means.
d. Use this equation to predict the number of women in the House of Representatives in the year 2013.

Question 68

My spouse was recently in Mexico, and I had to determine the cheapest way to call. AT&T has an international wireless plan called World Connect with a monthly fee of $3.99, and then my calls to a Mexican landline are $0.09 per minute. Without this plan, I would pay no monthly fee and $0.49 per minute.
a. Write equations for the cost C of each option.
I'm using the letter _______________ to represent the variable quantity __________.
b. Solve the system of equations you wrote in part a to find the number of minutes for which the two options would cost the same. (Round to the nearest whole minute.)When would it make sense to pay for the World Connect plan?

Question 69

L varies jointly as a and the square root of b . If L=160 when a=5 and b=16 , find L when and b=144 .

A) L=384
B) L=32
C) L=4
D) L=96

Question 70

The following table shows the cost of renting a full-size rental car, based on the number of miles
driven.
a. Explain why a linear equation is appropriate for this relationship.
b. Find the slope of the line and explain what it means.
c. Find the y-intercept and explain what it means.
d. Determine the equation of the line.
e. Is this a direct variation relationship? Why or why not? Be specific.
f. I am trying to decide whether I can afford to rent a full-size car to drive to St. Louis, which is about 180
miles away. How much would that cost for a one-way trip? How much would it cost for a round trip of 360
miles?
g. Why doesn't the round trip cost twice as much as the one-way trip? Be specific.

Question 71

True story from Erin's life: My 4-month old daughter got her shots, and we ended up needing to give her some tylenol for the pain. Infant Tylenol comes in liquid form, and the box indicates that there are 160 mg of
acetaminophen per 5 mL of liquid.
a. Complete the table, and then use it to draw a graph, where x is the amount of infant Tylenol in mL and y is the amount of acetaminophen in mg.
b. Is this a direct variation relationship? Why or why not? Be specific.
c. Find the slope of the line you graphed and explain what it means.
d. Write a linear equation that describes the amount of acetaminophen in mg (y)in terms of mL of infant tylenol (x).
e. In spite of the handy SimpleMeasure syringe, the directions don't give a dosage for children
under 2 years old. This is because it depends on weight and they want you to call the doctor so you don't get the math wrong. But I'm a math teacher, so I looked it up. For my daughter's weight at that time, the dosage is 115 mg of acetaminophen. How many mL of infant Tylenol did I need to give her?