Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and 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, indicating how much y changes for a unit change in x.

Front

How do you calculate 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 is the y-intercept in a linear function?

Back

The y-intercept is the value of y when x = 0, represented by the 'b' in the equation y = mx + b.

Front

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

Back

A slope of 0 indicates that the function is constant; the value of y does not change as x changes.

Front

What is the difference between a positive and negative slope?

Back

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

Front

How can you determine if one linear function is cheaper than another at a specific point?

Back

To determine which function is cheaper, substitute the x-value into both equations and compare the resulting y-values.

Front

What does it mean if two linear functions have the same slope?

Back

If two linear functions have the same slope, they have the same rate of change, but they may have different y-intercepts.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

How do you graph a linear function?

Back

To graph a linear function, plot the y-intercept on the y-axis, use the slope to find another point, and draw a straight line through the points.