The equation
models the relation between the amount of Tuyet’s monthly water bill payment,
P , in dollars, and the number of units of water,
w , used.
-
ⓐ Find Tuyet’s payment for a month when 0 units of water are used.
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ⓑ Find Tuyet’s payment for a month when 12 units of water are used.
-
ⓒ Interpret the slope and
P -intercept of the equation.
-
ⓓ Graph the equation.
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The equation
models the relation between the amount of Randy’s monthly water bill payment,
P , in dollars, and the number of units of water,
w , used.
-
ⓐ Find the payment for a month when Randy used 0 units of water.
-
ⓑ Find the payment for a month when Randy used 15 units of water.
-
ⓒ Interpret the slope and
P -intercept of the equation.
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ⓓ Graph the equation.
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ⓐ $28
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ⓑ $66.10
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ⓒ The slope, 2.54, means that Randy’s payment,
P , increases by $2.54 when the number of units of water he used,
w, increases by 1. The
P –intercept means that if the number units of water Randy used was 0, the payment would be $28.
-
ⓓ
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Bruce drives his car for his job. The equation
models the relation between the amount in dollars,
R , that he is reimbursed and the number of miles,
m , he drives in one day.
-
ⓐ Find the amount Bruce is reimbursed on a day when he drives 0 miles.
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ⓑ Find the amount Bruce is reimbursed on a day when he drives 220 miles.
-
ⓒ Interpret the slope and
R -intercept of the equation.
-
ⓓ Graph the equation.
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Janelle is planning to rent a car while on vacation. The equation
models the relation between the cost in dollars,
C , per day and the number of miles,
m , she drives in one day.
-
ⓐ Find the cost if Janelle drives the car 0 miles one day.
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ⓑ Find the cost on a day when Janelle drives the car 400 miles.
-
ⓒ Interpret the slope and
C –intercept of the equation.
-
ⓓ Graph the equation.
-
ⓐ $15
-
ⓑ $143
-
ⓒ The slope, 0.32, means that the cost,
C , increases by $0.32 when the number of miles driven,
m, increases by 1. The
C -intercept means that if Janelle drives 0 miles one day, the cost would be $15.
-
ⓓ
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Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation
models the relation between her weekly salary,
S , in dollars and the amount of her sales,
c , in dollars.
-
ⓐ Find Cherie’s salary for a week when her sales were 0.
-
ⓑ Find Cherie’s salary for a week when her sales were 3600.
-
ⓒ Interpret the slope and
S –intercept of the equation.
-
ⓓ Graph the equation.
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Patel’s weekly salary includes a base pay plus commission on his sales. The equation
models the relation between his weekly salary,
S , in dollars and the amount of his sales,
c , in dollars.
-
ⓐ Find Patel’s salary for a week when his sales were 0.
-
ⓑ Find Patel’s salary for a week when his sales were 18,540.
-
ⓒ Interpret the slope and
S -intercept of the equation.
-
ⓓ Graph the equation.
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ⓐ $750
-
ⓑ $2418.60
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ⓒ The slope, 0.09, means that Patel’s salary,
S , increases by $0.09 for every $1 increase in his sales. The
S -intercept means that when his sales are $0, his salary is $750.
-
ⓓ
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Costa is planning a lunch banquet. The equation
models the relation between the cost in dollars,
C , of the banquet and the number of guests,
g .
-
ⓐ Find the cost if the number of guests is 40.
-
ⓑ Find the cost if the number of guests is 80.
-
ⓒ Interpret the slope and
C -intercept of the equation.
-
ⓓ Graph the equation.
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Margie is planning a dinner banquet. The equation
models the relation between the cost in dollars,
C of the banquet and the number of guests,
g .
-
ⓐ Find the cost if the number of guests is 50.
-
ⓑ Find the cost if the number of guests is 100.
-
ⓒ Interpret the slope and
C –intercept of the equation.
-
ⓓ Graph the equation.
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ⓐ $2850
-
ⓑ $4950
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ⓒ The slope, 42, means that the cost,
C , increases by $42 for when the number of guests increases by 1. The
C -intercept means that when the number of guests is 0, the cost would be $750.
-
ⓓ
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Use Slopes to Identify Parallel Lines
In the following exercises, use slopes and y-intercepts to determine if the lines are parallel.
Use Slopes to Identify Perpendicular Lines
In the following exercises, use slopes and y-intercepts to determine if the lines are perpendicular.
Everyday math
The equation
can be used to convert temperatures
F , on the Fahrenheit scale to temperatures,
C , on the Celsius scale.
-
ⓐ Explain what the slope of the equation means.
-
ⓑ Explain what the
C –intercept of the equation means.
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The equation
is used to estimate the number of cricket chirps,
n , in one minute based on the temperature in degrees Fahrenheit,
T .
-
ⓐ Explain what the slope of the equation means.
-
ⓑ Explain what the
n –intercept of the equation means. Is this a realistic situation?
-
ⓐ For every increase of one degree Fahrenheit, the number of chirps increases by four.
-
ⓑ There would be
chirps when the Fahrenheit temperature is
. (Notice that this does not make sense; this model cannot be used for all possible temperatures.)
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Writing exercises
Self check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ After looking at the checklist, do you think you are well-prepared for the next section? Why or why not?
