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

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is the y-intercept of the equation y = 4x + 2?

Back

The y-intercept is 2, which is the value of y when x = 0.

Front

How do you compare the slopes of two linear equations?

Back

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

Front

What is the slope of the equation y = -3x + 5?

Back

The slope is -3.

Front

If two linear functions have the same slope, what does that imply?

Back

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

Front

What does it mean if a linear function has a positive slope?

Back

A positive slope means that as x increases, y also increases, indicating a direct relationship.

Front

What does it mean if a linear function has a negative slope?

Back

A negative slope means that as x increases, y decreases, indicating an inverse relationship.

Front

How can you determine which linear function has a greater rate of change?

Back

The function with the larger absolute value of the slope has a greater rate of change.