Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 of a linear function represents the rate of change of the function. It indicates 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 point where the line crosses the y-axis. It is the value of y when x = 0.

Front

How do you determine which linear function is cheaper at a given value of x?

Back

To determine which linear function is cheaper at a given value of x, substitute x into both equations and compare the resulting y values.

Front

What is the equation of Nate's service?

Back

y = 4x + 6

Front

If Beth's service costs $38 for 8 movies, what is the equation for Beth's service?

Back

To find the equation, use the point (8, 38) and the slope. If we assume a similar slope as Nate's, it could be y = mx + b.

Front

How do you compare the rates of change of two linear functions?

Back

Compare the slopes (m values) of the two functions. The function with the greater slope has a greater rate of change.

Front

What is the rate of change for the equation y = 3x - 1?

Back

The rate of change (slope) is 3.

Front

What is the rate of change for the equation y = 1/2x + 1?

Back

The rate of change (slope) is 1/2.

Front

Which equation has a higher y-intercept: y = 3x - 1 or y = 1/2x + 1?

Back

y = 1/2x + 1 has a higher y-intercept of 1.