Linear Functions Review

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 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 value of y when x is 0. It represents the starting point of the function on the y-axis.

Front

How do you determine if a function is linear or nonlinear?

Back

A function is linear if it can be expressed in the form y = mx + b. If the graph of the function is not a straight line, it is nonlinear.

Front

What does it mean if a function has a positive slope?

Back

A positive slope indicates that as x increases, y also increases. The function is rising.

Front

What does it mean if a function has a negative slope?

Back

A negative slope indicates that as x increases, y decreases. The function is falling.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the significance of the y-intercept in real-world scenarios?

Back

The y-intercept often represents the initial value or starting point of a situation before any changes occur.

Front

How can you identify the rate of change from a word problem?

Back

The rate of change can often be found by determining how much one quantity changes in relation to another, typically expressed as a ratio.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.