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

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

Back

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

Front

What is the difference between positive and negative slopes?

Back

A positive slope means the line rises as it moves from left to right, while a negative slope means the line falls as it moves from left to right.

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.

Front

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

Back

You can compare the coefficients of x in the equations. The function with the larger coefficient has a greater slope.

Front

What is the y-intercept of the equation y = 4x + 5?

Back

The y-intercept is 5, which is the value of y when x = 0.

Front

If two linear functions intersect, what does that indicate?

Back

If two linear functions intersect, it indicates that they have different slopes and will meet at a specific point.

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).

Front

What does a slope of zero indicate about a linear function?

Back

A slope of zero indicates that the linear function is a horizontal line, meaning there is no change in y as x changes.