Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, defined by the equation 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, indicating how much y changes for a unit change in x.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the value of y when x is 0, representing the point where the line crosses the y-axis.

Front

How can you determine if a function is linear from a table of values?

Back

A function is linear if the differences between consecutive y-values are constant for equal intervals of x.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph to a straight line, while nonlinear functions do not have a constant rate of change and graph to a curve.

Front

If a function's output increases by 3 for every increase of 1 in the input, what is the slope?

Back

The slope is 3.

Front

What does it mean if a function is described as nonlinear?

Back

It means that the function does not have a constant rate of change and its graph is not a straight line.

Front

In the equation y = 2x + 5, what is the slope?

Back

The slope is 2.

Front

What is the significance of the x-intercept?

Back

The x-intercept is the value of x when y is 0, representing the point where the line crosses the x-axis.

Front

How do you find the y-intercept from a linear equation?

Back

To find the y-intercept, set x to 0 in the equation and solve for y.