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 the y-value changes for a unit change in the x-value.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

Write the linear function for Jerome's savings after x months.

Back

J(x) = 40x + 150.

Front

How do you solve for x in the equation C(x) = 23 for the cell phone cost?

Back

Set the equation 2x + 15 = 23, then solve for x to find x = 4 minutes.

Front

What is the slope of the line represented by the equation y = 3x + 6?

Back

The slope is 3.

Front

What is the equation of a line in slope-intercept form?

Back

The equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

Is the function C(x) = 2x + 15 linear or nonlinear?

Back

Linear.

Front

If the slope of a line is 3 and the y-intercept is 6, what is the equation?

Back

y = 3x + 6.

Front

What does it mean if a function is nonlinear?

Back

A nonlinear function does not graph to a straight line and may involve curves or other shapes.