Find the Slope and What It Represents
A plant grows 24 cm in 6 weeks at a constant rate. What is the slope, and what does it represent?
m=2.
It represents the plant grows 2 cm per week.
What is the y-intercept, and what does it represent?
Time (min). Water left in tank (gallons)
0 50
2 44
4 38
b=50.
It represents the tank started with 50 gallons.
A babysitter earns $12 per hour plus a $5 tip each night. Write an equation for the total money y after x hours.
y = 12x + 5
Store A sells apples for $3 per pound. Store B sells 4 pounds for $10. Which store has the better price per pound?
Store B.
Store B costs $2.50 per pound, and Store A costs $3 per pound.
What is the slope, and what does it represent?
Hours worked Pay($)
2 30
4 60
6 90
m=15
It represents the person gets paid $15 per hour worked
A taxi charges a $3 flat fee plus $2 per mile. What is the y-intercept, and what does it represent?
b=3.
It represents the flat fee the taxi charges before riding any miles.
Write the equation for this table, if x is days and y is the number of pages left in a book.
# of days Pages left in book
0 40
2 34
4 28
6 22
y = -3x + 40
Plan A costs $30 per month.
Plan B is shown in the table. Which plan is the better deal per month?
Months Plan B cost ($)
2 50
4 100
6 150
Plan B.
Plan B costs $25 per month, and Plan A costs $30 per month.
What is the slope, and what does it represent?
Hours burning. Candle height (in)
4 12
6 9
8 6
m= -3/2
It represents the height of the candle is decreasing 3/2 inches every hour.
A food truck uses a large propane tank to heat its grills. The tank holds 100 pounds of propane when completely full and burns through the fuel at a constant rate of 1 pound every 8 minutes of cooking.
What is the y-intercept, and what does it represent?
b=100.
It represents the starting amount of propane in the tank was 100 pounds before the cooking started.
A hot air balloon is at 200 feet and descends at a constant rate of 15 feet per minute. Write an equation for the balloon’s height y after x minutes.
y = -15x + 200
Two cousins, Ava and Ben, are tracking their heights. Ava’s height in inches is y = 2x + 55, where x is years. Ben’s height in inches is y = 3x + 50, where x is years.
Who is growing faster, and by how much?
Ava’s slope of 2 means she grows 2 inches per year. Ben’s slope of 3 means he grows 3 inches per year.
Ben is growing faster, by 1 inch per year.
A family is driving on a road trip. Because of heavy traffic and construction, they check their navigation app twice to see how much distance they have left to drive.
What is the slope, and what does it represent?
m= -15
It represents the distance decreases by 15 miles per hour.
What is the y-intercept, and what does it represent?
Time (min) Water in Tank (gallons)
2 44
4 38
6 32
b=50.
It represents there was 50 gallons of water in the tank to start with.
A phone is charged to 80% and drains 5% every hour while a student plays a game. Write an equation for the battery percent y after x hours.
y = -5x + 80.
Gym A costs y = 5x + 20, where x is months. Gym B has a $10 sign-up fee plus $8 per month. Which gym costs less for 6 months?
Gym A
Gym A cost: y=5(6)+20 = 50
Gym B cost: y=8(6)+10 = 58