Mathematician: ___________________________________Date: ____________________Per. _______________
Real Life Scenarios
1. The cost of c (in dollars) to rent a bicycle is proportional to the number h of hours that you
rent the bicycle. It costs $20 to rent the bicycle for 4 hours.
a. Write an equation that represents the situation.
b. Interpret the slope.
c. How much does it cost to rent the bicycle?
2. You sold a total of $16 worth of cheese. You forgot how many pounds of each type of
cheese you sold. Swiss: $4/ lb.; Cheddar: $2/ lb.
A . let x represent the number of pounds of Swiss cheese. Let y represent the number of
pounds of cheddar cheese. Write an equation in Standard Form that relates x and y.
b. Rewrite the equation in slope-intercept form. Then, graph the equation.
c. You sold 2 pounds of Cheddar cheese. How many pounds of Swiss cheese did you sell?
d. Does the value x = 2.5 make sense in the context of the problem? Explain.
3. You go shopping and buy x shirts for $12 and y jeans for $28. The total spent is $84.
a. Write and equation in standard form that models how much money you spent.
b. Graph the equation and interpret the intercepts.
x-Intercept: ____________________________________
y-intercept: ____________________________________
4. The graph shows a trip taken by a car, where t is the time (in hours) and y is the distance
(in miles) from phoenix.
a. Find the y-intercept of the graph. What does it represent?
b. Find the slope of the graph. What does it represent?
c. How long did the trip last?
d. How far from Phoenix was the car at the end of the trip?
e. Write an equation that represents the graph (slope-intercept form).
5. You organize a garage sale. You have $30 at the beginning of the sale. You earn an average
of $20 per hour. Write an equation (slope-intercept) that represents the amount of money y
you have after x hours.
6. The total cost for bowling includes the fee for shoe rental plus a fee per game. The cost of
each game increases the price by $4. After 3 games, the total cost with shoe rental is $14.
a. Write an equation to represent the total cost y to rent shoes and bowl x games.
b. How much is shoe rental? How is this represented in the equation?
7.
a. What does the graph show?
b. Estimate the y-intercept. What
does it represent?
c. Estimate the slope. What does it
represent?
d. Write an equation to represent oven temperature y to time x .
e. Use the equation to find the oven temperature after 6 minutes.
f. Use the equation to find how long it will take for the oven temperature to reach
200 degrees.
8. A plant is 3 inches tall when you purchase it and grows 2 inches per month.
Write an equation that represents the height y (in inches) of a plant that you
purchased x months ago.
9. A bucket is empty. You are filling the bucket with water at a rate of
3 inches per second.
a. Plot the points 0, 0 and 5, 15.
b. What do the points in part (a) represent?
c. Draw a line through the points.
d. What does the line represent?
e. Write an equation of the line.
10. You are planning to make a scrapbook. The album costs $20 and each of the scrapbook
papers costs an additional $1. Write an equation that represents the cost of the completed
scrapbook papers you purchase.
11. A hot tub that holds 300 gallons of water drains at a rate of 8 gallons per minute. Write an
equation that represents how many gallons of water are left in the tub after it has drained for
x minutes.
12. An elevator in a tall building is at a point 180 feet above the ground. The elevator descends
at a rate of 12 feet per second. Write an equation that represents how far above the ground
the elevator is after descending for x seconds.
13. After a laptop is purchased, its value decreases by $150 each year. After 2
years, the laptop is worth $600.
a. Write an equation that represents the value V (in dollars) of the laptop x
years after it is purchased.
b. What was the original value of the laptop?
c. What is the value of the laptop 5 years after it is purchased?
14. The grade of a ski trail describes the steepness of the ski slope. A skier can calculate the
grade by dividing the vertical decrease (in meters) of the slope by the horizontal distance (in
meters) it covers.
Frosty’s Ski Center
a. How does the grade of a trail relate to the slope of a line?
b. What is the slope of each of the ski trails?
Trail
Grade of Trail
Bunny Slope
4%
Medium Trail
15%
Expert Route
30%
c. There is a first aid station located at the point (750, 28) on the Bunny Slope. Write an
equation that describes the Bunny Slope.
d. What is the y-intercept of your equation? What does the y-intercept mean in terms of the
Bunny Slope?
e. What is the x-intercept of your equation? What does the x-intercept mean in terms of the
Bunny Slope?
f. The halfway point on the Medium Trail is located at (5100, 765). Write an equation that
describes the Medium Trail.
g. The Expert Route passes by the ski lodge located at the point (15,000, 1500). Write an
equation that describes the Expert Route.
h. Beginner slopes for new skiers have a maximum grade of 5%. Two skiers on a trail are
located at the points (700, 30) and (450, 50). Is the trail a beginner slope? Explain.