Book 5 Unit Test Review Questions
pp. 19 - 24
10) Similarities: In Tables 1 and 2, the x values increase by one; this isn’t true in Tables 3
and 4. Differences: In Table 1, the value of y doesn’t change at all; in Tables 2, 3, and 4,
it does. In Table 2, the y-values decrease and then increase; in Table 3, the y-values
increase; and in Table 4, they decrease. In Tables 1, 3, and 4, as the x-values go up by 1,
the y -value changes at a constant rate; this isn’t true in Table 2. Note: The patterns in
Tables 1, 3, and 4 are similar in that, as x goes up by 1, the y-values change by the
following patterns: 0, 0, 0, . . . in Table 1; 3, 3, 3, . . . in Table 3; and −1.5, −1.5, −1.5, . .
. for Table 4. So, the data in Tables 1,3, &4 are linear. The graph of Table 2 is nonlinear.
(Actually, its graph is a parabola; it is in fact quadratic.) Its table indicates this
nonlinearity by the nonconstant rate of change between y-values as x increases by 1.
Tables 1, 3, and 4 represent linear relationships. The change in the y-value is the same for
each unit change in the x-value, and the graph forms a straight line.
Table 1: y=3;Table 3: y=3x+10Table 4: y=−1.5x−3; In Table 1, the y-value is 3 for
any x-value. In Table 3, the x-value increases by 3 for every y increase of 1.
When x=0,y=10. In Table 4, the y-value decreases by 1.5 as the x-value increases by 1.
The y-value is –3 when x=0.
11) t = 30 − 5h; The variable t represents the temperature in degrees Fahrenheit, which
will be 30° minus the 5° per hour (h) that the temperature is expected to drop.
This is a linear relationship. The constant rate of change is –5.That is, as the hours
increase by 1, the temperature decreases by 5.
(13) Graph 1: y = −x and Graph 2: y = −x
(25) For about the first 3 seconds, John ran at a constant rate of l m/s. He then paused for
a second and slowly increased his rate for about 3 seconds to run 3 meters, then ran at a
constant rate of 2 m/s for one second, paused for 3 seconds, and finished the race at a rate
of 3 m/s. He did not run at a constant rate for the entire race.
(26) No, it is not linear; there is not a constant rate of change. There are 4 different rates
of change represented in the graph.
Yes; a person starts off walking for 5 seconds at a constant rate, stops for 3 seconds, then
walks at a constant rate for 2 seconds, and then walks a little faster at a constant rate.
(27) At 70 seconds, about 20 milliliters has been lost, so an estimated time that the
100-ml container would be full is 70×5=350seconds, or 5 minutes and 50 seconds.
The relationship between water loss and time is fairly close to linear, but it is not exactly
linear. It isn’t linear since the rate is not constant. For example, the time is going up by
even intervals of 10 seconds. The patterns of change in the water loss for the first few
values are 5−2=3 and 8.5−5=3.5. Since 3 is not equal to 3.5, there is no constant rate.
pp. 41 - 46
(6) a. about 75 protein bars
Note: Students are reading answers from the graph, so some inaccuracy is expected.
b. $33.50 because 0.67(50)=33.5; $83.75 because 0.67(125)=83.75
Note: The 0.67 was derived from the points (0,0) and (300,200), showing that each
protein bar would sell for $0.67.
c. For an income of $200, the band would have to sell about 300 protein bars. The cost
would be $125, leaving a profit of about $75.
Note: Using 300 as the amount of bars and $0.34 as the cost of the bars, the answer is
$73.
(7) The graphs in a and b are linear. The equation for a is y = 3x + 1, and the equation
for b is y=2x+7. The patterns in c and d are not linear, because there is no constant rate of
change.
(10) plan 1: $140.40; Plan 2: $78
Both plans require 25 weeks.
Plan 1: y = 270 − 10.8x; Plan 2: y = 150 −6x; y represents the amount of money you
owe, and x represents the number of weeks. The 270 and the 150 represent the amount
owed after making the down payment (if any down payment), and the 10.8 and the 6
represent how much you pay every week.
The amount of money owed after 12 weeks would increase: Plan 1: $225.40; Plan 2:
$163. Plan 1 requires the least number of weeks to pay off the skateboard now. It
requires a little more than 32 weeks, while Plan 2 requires a little over 39 weeks to pay
for the skateboard.
The equations are now: Plan 1: y = 355 − 10.8x; Plan 2: y = 235 − 6x; y represents the
money you owe, and x represents the number of weeks. The 355 and the 235 represent
the amount owed after making the down payment (if any down payment), and the 10.8
and the 6 represent how much you pay every week.
(17) a.Graph 3; b.Graph 4; c.Graph 2; y = −2x + 4
(30) a.True; b.False; 5(0.7x+5)= 3.5x + 25, not 3.5x + 5; c.True
pp. 72 - 75
(18) a. x = −2.5; b. x = 4.5; c. x = −5.5; d. x = −2.5
(19) a. x = 1; b. x = 2; c. x = 1; d. x = 1
(32) The break-even point for the two plans is 400 texts. So, Walby
Communications is cheaper for t > 400 and Driftless is cheaper for t < 400.
If you graph each of the plans, the cheaper plan has the line in the lower position
before or after 400 texts.