Comparing 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 linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

How do you determine the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a linear function?

Back

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

Front

What does a negative slope indicate about a linear function?

Back

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

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

How can you compare the slopes of two linear functions?

Back

You can compare the slopes by looking at the coefficients of x in their equations. The function with the larger coefficient has a steeper slope.

Front

If two linear functions have the same slope, what can you say about their rates of change?

Back

If two linear functions have the same slope, they have the same rate of change.

Front

What does it mean if two linear functions are parallel?

Back

Two linear functions are parallel if they have the same slope but different y-intercepts.

Front

What does it mean if two linear functions intersect?

Back

If two linear functions intersect, it means they have different slopes and will cross at one point.