Comparing 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 of a linear function represent?

Back

The slope represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

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

Front

How do you determine the rate of change from a linear equation?

Back

The rate of change can be determined from the slope (m) in the equation y = mx + b.

Front

What does it mean if two linear functions have the same slope?

Back

If two linear functions have the same slope, they have the same rate of change, meaning they increase or decrease at the same rate.

Front

How can you tell which linear function is increasing faster?

Back

The function with the greater slope (m) is increasing faster.

Front

What is the equation of a linear function that represents a monthly fee of $10 plus $3 per visit?

Back

y = 3x + 10.

Front

If a linear function has a slope of 0, what does that indicate?

Back

A slope of 0 indicates that the function is constant; y does not change as x changes.

Front

What is the significance of the x-intercept in a linear function?

Back

The x-intercept is the value of x when y is 0. It indicates where the graph crosses the x-axis.

Front

How do you find the total cost from a linear function representing costs?

Back

You substitute the number of units (x) into the function to find the total cost (y).