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

What is the y-intercept of a linear function?

Back

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

Front

How do you determine which linear function has a greater y-intercept?

Back

To determine which linear function has a greater y-intercept, compare the values of b in the equations of the functions.

Front

What does it mean if two linear functions have the same slope?

Back

If two linear functions have the same slope, they are parallel to each other and will never intersect.

Front

How can you tell if a linear function is increasing or decreasing?

Back

A linear function is increasing if the slope (m) is positive and decreasing if the slope (m) is negative.

Front

What is the significance of a negative slope in a linear function?

Back

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

Front

How do you find the slope between two points on a graph?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for two linear functions to intersect?

Back

If two linear functions intersect, it means they have a common solution (x, y) where both equations are true.