P.2 Linear Models and Rates of Change 11
P.2 Linear Models and Rates of Change
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Estimate the slope of the line from the graph.
a. 3
b.
c.
d.
e. 6
____ 2. Sketch the line passing through the point (3, 4) with the slope .
a. d.
12 Chapter P: Preparation for Calculus
b. e.
c.
____ 3. Find the slope of the line passing through the pair of points.
a.
b.
c.
d. 0
e.
P.2 Linear Models and Rates of Change 13
____ 4. Find the slope of the line passing through the points and .
a. 63
b. 21
c. 42
d. 21
e. 42
____ 5. If a line has slope and passes through the point , through which of the
following points does the line also pass?
a.
b.
c.
d.
e.
____ 6. A moving conveyor is built to rise 5 meters for every 7 meters of horizontal change.
Find the slope of the conveyor.
a. 0
b.
c.
d.
e.
____ 7. A moving conveyor is built to rise 1 meter for every 5 meters of horizontal change.
Suppose the conveyor runs between two floors in a factory. Find the length of the conveyor if the
vertical distance between floors is 10 meters. Round your answer to the nearest meter.
a. 61 meters
b. 39 meters
c. 51 meters
d. 50 meters
e. 41 meters
14 Chapter P: Preparation for Calculus
____ 8. Find the slope of the line .
a.
b.
c.
d.
e.
____ 9. Find the y-intercept of the line .
a.
b.
c.
d.
e.
____ 10. Find an equation of the line that passes through the point and has the slope m
that is undefined.
a.
b.
c.
d.
e.
____ 11. Find an equation of the line that passes through the point and has the slope
.
a. –
b. +
c. + 162
d.
e.
P.2 Linear Models and Rates of Change 15
____ 12. Find an equation of the line that passes through the points and .
a.
b.
c.
d.
e.
____ 13. Find an equation of the line that passes through the points and
.
a.
b.
c.
d.
e.
____ 14. Use the result, “the line with intercepts has the equation ,
, ”, to write an equation of the line with x-intercept: and y-intercept: .
a.
b.
c.
d.
e.
16 Chapter P: Preparation for Calculus
____ 15. Sketch a graph of the equation .
a. d.
b. e.
c.
P.2 Linear Models and Rates of Change 17
____ 16. Write an equation of the line that passes through the given point and is perpendicular
to the given line.
a.
b.
c.
d.
e.
____ 17. Write an equation of the line that passes through the given point and is parallel to the
given line.
a.
b.
c.
d.
e.
____ 18. Write an equation of the line that passes through the point and is
perpendicular to the line .
a.
b.
c.
d.
e.
____ 19. Write an equation of the line that passes through the point and is parallel to
the line .
a.
b.
c.
d.
e.
18 Chapter P: Preparation for Calculus
____ 20. A real estate office handles an apartment complex with units. When the rent is
per month, all units are occupied. However, when the rent is , the average number of
occupied units drops to . Assume that the relationship between the monthly rent and the demand
is linear. Write a linear equation giving the demand in terms of the rent .
a.
b.
c.
d.
e.
____ 21. A real estate office handles an apartment complex with units. When the rent is
per month, all units are occupied. However, when the rent is $ , the average number of
occupied units drops to . Assume that the relationship between the monthly rent and the demand
is linear. Predict the number of units occupied if the rent is raised to .
a. 43 units
b. 54 units
c. 57 units
d. 49 units
e. 46 units
____ 22. Find the distance between the point and line using the formula,
for the distance between the point and the line
.
a.
b.
c.
d.
e.
P.2 Linear Models and Rates of Change 19
____ 23. Suppose that the dollar value of a product in is and the rate at which the
value of the product is expected to increase per year during the next years is . Write a linear
equation that gives the dollar value of the product in terms of the year . (Let represent .)
Round the numerical values in your answer to one decimal place, where applicable.
a.
b.
c.
d.
e.
____ 24. A company reimburses its sales representatives per day for lodging and meals
plus ¢ per mile driven. Write a linear equation giving the daily cost to the company in terms of ,
the number of miles driven. Round the numerical values in your answer to two decimal places, where
applicable.
a.
b.
c.
d.
e.
____ 25. A company reimburses its sales representatives per day for lodging and meals
plus ¢ per mile driven. How much does it cost the company if a sales representative drives
miles on a given day? Round your answer to the nearest cent.
a. 227.20
b. 216.70
c. 136.35
d. 161.35
e. 191.70
20 Chapter P: Preparation for Calculus
P.2 Linear Models and Rates of Change
Answer Section
MULTIPLE CHOICE
P.2 Linear Models and Rates of Change 21