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 slope from two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

If a linear function has a slope of 0, what does that mean?

Back

A slope of 0 means the function is a horizontal line, indicating that there is no change in y as x changes.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship between the two variables.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

How can you determine which of two linear functions has a greater slope?

Back

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

Front

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

Back

The slope of the equation y = 4x + 2 is 4.

Front

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

Back

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