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 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 the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the y-intercept of a linear function?

Back

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

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, meaning they increase or decrease at the same rate.

Front

How can you tell which linear function has a greater rate of change?

Back

The function with the greater slope (m) has a greater rate of change. A steeper line indicates a larger slope.

Front

What is the difference between a positive slope and a negative slope?

Back

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

Front

What is the initial fee in a linear cost function?

Back

The initial fee is the fixed cost that does not change with the number of units (e.g., guests) and is represented by the y-intercept (b) in the equation.

Front

How do you compare the rates of change of two linear functions?

Back

To compare the rates of change, look at the slopes of the functions. The function with the larger slope has a greater rate of change.

Front

What is a real-world example of a linear function?

Back

A real-world example of a linear function is the cost of a taxi ride, where there is a base fare (initial fee) plus a charge per mile (slope).