Comparing Linear Functions

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 of a linear function represents the rate of change of the dependent variable (y) with respect to the independent variable (x). 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 value of the dependent variable.

Front

How do you calculate the rate of change between two points on a linear function?

Back

The rate of change (slope) between two points (x1, y1) and (x2, y2) is calculated using the formula: (y2 - y1) / (x2 - x1).

Front

If a linear function has a slope of 0, what does that indicate?

Back

A slope of 0 indicates that the function is a horizontal line, meaning there is no change in y as x changes.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship between the two variables.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

In the equation y = 2x + 5, what is the slope and what does it represent?

Back

The slope is 2, which represents that for every 1 unit increase in x, y increases by 2 units.

Front

In the equation y = -3x + 4, what does the y-intercept represent?

Back

The y-intercept is 4, which means that when x is 0, the value of y is 4.

Front

How can you determine if two linear functions have the same rate of change?

Back

Two linear functions have the same rate of change if their slopes are equal.