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 function. It indicates how much the y-value changes for a unit change in the x-value.

Front

How do you find the slope from a table of values?

Back

To find the slope from a table of values, use the formula: slope (m) = (change in y) / (change in x) between two points.

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the same as the slope. It indicates how steep the line is and the direction it goes.

Front

If a linear function has a positive slope, what does that indicate about the function?

Back

A positive slope indicates that as x increases, y also increases, meaning the function is increasing.

Front

If a linear function has a negative slope, what does that indicate about the function?

Back

A negative slope indicates that as x increases, y decreases, meaning the function is decreasing.

Front

What is the y-intercept of 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

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 (m values) are equal.

Front

What is the slope of the function represented by the equation y = 3x - 4?

Back

The slope of the function y = 3x - 4 is 3.

Front

How do you convert the equation 3x - 5y = 25 to slope-intercept form?

Back

To convert to slope-intercept form, solve for y: 5y = 3x - 25, then y = (3/5)x - 5.