Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 find the y-intercept of a linear equation?

Back

To find the y-intercept of a linear equation in the form y = mx + b, set x to 0 and solve for y. The value of y when x = 0 is the y-intercept.

Front

What is the difference between positive and negative slopes?

Back

A positive slope indicates that as x increases, y also increases. A negative slope indicates that as x increases, y decreases.

Front

How can you compare the slopes of two linear functions?

Back

To compare the slopes of two linear functions, look at the coefficients of x in their equations. The function with the larger coefficient has a steeper slope.

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 and will never intersect unless they also have the same y-intercept.

Front

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

Back

The y-intercept of the equation y = 4x + 2 is 2, which is the value of y when x = 0.

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 constant term (b) in the equations of the functions.

Front

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

Back

The slope of the line represented by the equation y = -3x + 5 is -3.

Front

If two lines intersect, what can be said about their slopes?

Back

If two lines intersect, their slopes are different, meaning they are not parallel.