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 the y-value changes for a one-unit increase in the x-value.

Front

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

Back

To determine which linear function has a greater slope, compare the coefficients of x in their equations. The function with the larger coefficient has the greater slope.

Front

What is the y-intercept in 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 is 0.

Front

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

Back

A linear function with a slope of 0 is a horizontal line, meaning there is no change in y as x changes.

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

How can you tell if a linear function is increasing or decreasing?

Back

A linear function is increasing if its slope is positive and decreasing if its slope is negative.

Front

What does it mean for two linear functions to be parallel?

Back

Two linear functions are parallel if they have the same slope but different y-intercepts.

Front

What does it mean for two linear functions to be perpendicular?

Back

Two linear functions are perpendicular if the product of their slopes is -1.

Front

How can you find the equation of a linear function given a slope and a point?

Back

You can use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.