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 line represent?

Back

The slope of a line represents the rate of change of the y-value with respect to the x-value. It indicates how steep the line is.

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 of 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

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

Back

If two linear functions have the same slope, they are parallel to each other and will never intersect.

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

Front

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

Back

You can compare the slope values (m) of the functions. The function with the larger m value has the greater slope.

Front

What is the significance of the initial fee in a cost function?

Back

The initial fee is a fixed cost that must be paid regardless of the number of units (e.g., guests) and affects the total cost.

Front

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

Back

In a real-world context, the slope can represent rates, such as cost per hour or growth rate, indicating how one quantity changes in relation to another.

Front

What is a cost function?

Back

A cost function is a mathematical representation that describes how the total cost changes with the number of units produced or services rendered.