Linear Functions - Proportional and Nonproportional

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 is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. Its graph can be curved or have varying slopes.

Front

What does it mean for a function to be proportional?

Back

A function is proportional if it can be expressed in the form y = kx, where k is a constant. In a proportional relationship, the ratio of y to x is constant.

Front

What does it mean for a function to be nonproportional?

Back

A function is nonproportional if it cannot be expressed in the form y = kx. In a nonproportional relationship, the ratio of y to x is not constant.

Front

How can you identify a linear function from its graph?

Back

A linear function can be identified by a straight line on the graph. If the graph curves or has bends, it is not linear.

Front

What is the slope of a line in a linear function?

Back

The slope of a line in a linear function represents the rate of change of y with respect to x. It is calculated as the rise over run.

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 represented by the value of b in the equation y = mx + b.

Front

Is the function y = 3x + 2 linear or nonlinear?

Back

Linear.

Front

Is the function y = x^2 + 1 linear or nonlinear?

Back

Nonlinear.

Front

What is the difference between proportional and nonproportional relationships?

Back

Proportional relationships have a constant ratio between y and x, while nonproportional relationships do not maintain a constant ratio.