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

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 the value of y when x = 0.

Front

How do you determine which linear function has a greater slope?

Back

Compare the coefficients of x in the equations. The function with the larger coefficient has a steeper slope.

Front

What is the slope of the equation y = 2x - 3?

Back

The slope is 2.

Front

What is the y-intercept of the equation y = 2x - 3?

Back

The y-intercept is -3.

Front

How do you find the y-intercept from the equation y = mx + b?

Back

The y-intercept is the value of b in the equation.

Front

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

Back

If they have the same slope but different y-intercepts, they are parallel lines.

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, which is the solution to the system of equations.

Front

How can you tell which linear function has a larger y-intercept?

Back

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