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 line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

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

Back

To find the y-intercept of a linear equation in the form y = mx + b, set x to 0 and solve for y. The y-intercept is the point where the line crosses the y-axis.

Front

What is the y-intercept in the equation y = -4x - 5?

Back

The y-intercept is -5.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions graph to straight lines, while nonlinear functions graph to curves or other shapes. Linear functions have a constant rate of change, whereas nonlinear functions do not.

Front

What is the slope of the line represented by the equation y = 3/2x + 3?

Back

The slope of the line is 3/2.

Front

What is the y-intercept of the equation y = 3/2x + 3?

Back

The y-intercept is (0, 3).

Front

What does the term 'rate of change' refer to in the context of linear functions?

Back

Rate of change refers to how much the dependent variable (y) changes for a unit change in the independent variable (x). It is represented by the slope of the line.

Front

If a function is described as linear, what can be inferred about its graph?

Back

If a function is linear, its graph will be a straight line.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.