Writing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What does the y-intercept (b) represent in a linear function?

Back

The y-intercept (b) is the value of y when x is 0. It represents the starting point of the function on the y-axis.

Front

Write the equation for the total cost of snowboarding if the hourly rate is $15 and the rental fee is $25.

Back

y = 15x + 25

Front

Write the equation for the total charges of car rental if the hourly rate is $8.50 and the rental fee is $25.50.

Back

y = 8.5x + 25.5

Front

Write the equation for the total cost of fruit if the basket costs $3 and each pound of fruit costs $2.50.

Back

y = 2.50x + 3

Front

Write the equation for the total amount of money Jerry has after working x hours if he starts with $20 and earns $7 per hour.

Back

y = 7x + 20

Front

If the total cost at an amusement park is modeled by y = 1.5x + 20, what is the entrance fee?

Back

The entrance fee is $20.

Front

How do you determine the total cost from a linear equation?

Back

To determine the total cost, substitute the value of x (number of hours, rides, etc.) into the equation and solve for y.

Front

What is the significance of the constant term in a linear function?

Back

The constant term (b) indicates the fixed cost or starting value of the function, independent of x.