Linear Functions Review

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, defined by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What does the y-intercept (b) represent in the equation y = mx + b?

Back

The y-intercept (b) represents the value of y when x is 0, indicating where the line crosses the y-axis.

Front

How can you determine if a relationship is linear from a table of values?

Back

A relationship is linear if the change in y divided by the change in x (the rate of change) is constant for all pairs of values.

Front

What is the average rate of change?

Back

The average rate of change is the change in the value of a function divided by the change in the input value over a specified interval.

Front

If a line has a slope of -5/4, what does this indicate about the line?

Back

A slope of -5/4 indicates that for every 4 units the line moves to the right, it moves down 5 units, showing a negative relationship.

Front

What is the formula for finding 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 it mean if a linear function has a positive slope?

Back

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

Front

What does it mean if a linear function has a negative slope?

Back

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

Front

How do you interpret the y-intercept in a real-world context?

Back

The y-intercept can represent a starting value or initial condition in a real-world scenario, such as the cost of an item before any additional charges.