Paul used his graduation money to start a landscaping business. He has made the same amount of money every month since opening his business, so his business profits can be represented with a linear function where x is the months since starting his business and y is the overall profits. His overall profits after 1, 2, 3, and 6 months are shown in the table. 1) What is the y intercept of the linear function that describes his business profits? What does this number represent in this example?

2) If Paul’s business continues to make the same amount of money each month, what would his profits be in 1 year?
Months since starting business (x)

Profits (y)

0

?

1

-$300

2

$125

3

$550

6

$1825

12

?

Level 3: Proficient (85%)

A hiker is walking down into a canyon at a steady rate. Her height above the canyon floor is shown in this the graph.

1) What are the domain and range of the function?

2) What are the x and y intercepts, and what do they represent?

3) Calculate the rate of change (slope, rise/run, m). What does it represent?

4) Write the equation of the line in slope-intercept form (y = mx + b)

Level 4: Distinguished (100%)

A 500-gallon tank full of water is draining at a rate of 12 gallons per minute.

How many gallons will be in the tank after 10 minutes?

How long will it take for the tank to have 200 gallons?

Write an equation that represents the relationship between the gallons of water in the tank and minutes the tank has been draining.

Graph your equation using graphing technology (ex: Desmos).

Mark the points on the graph that represent the gallons after 10 minutes? Write down the coordinates.

Mark the points on the graph that represent when the tank has 200 gallons. Write down the coordinates.

How long will it take until the tank is empty?

What do the slope, y-intercept, and x-intercept represent in this example?