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

Front

How do you find the y-intercept of a linear equation?

Back

The y-intercept can be found by setting x to 0 in the equation and solving for y.

Front

What is the difference between the slope and the y-intercept?

Back

The slope indicates the steepness of the line, while the y-intercept is the point where the line crosses the y-axis.

Front

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

Back

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

Front

How can you compare the slopes of two linear equations?

Back

You can compare the coefficients of x in the equations. The larger the coefficient, the steeper the slope.

Front

What does it mean if two linear functions are parallel?

Back

If two linear functions are parallel, 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, they have different slopes and will cross at one point.

Front

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

Back

Compare the constant term (b) in the equations. The function with the larger constant has the greater y-intercept.

Front

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

Back

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