Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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 y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

How do you determine the steepness of a slope?

Back

The steepness of a slope is determined by the absolute value of the slope (m) in the equation y = mx + b. A larger absolute value indicates a steeper slope.

Tags

CCSS.8.EE.B.5

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 represents the value of y when x is 0.

Front

If two linear functions have the same slope, what can be said about their steepness?

Back

If two linear functions have the same slope, they have the same steepness, regardless of their y-intercepts.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

What does it mean if a slope is negative?

Back

A negative slope indicates that as x increases, y decreases. The line slopes downward from left to right.

Tags

CCSS.8.EE.B.5

Front

What does it mean if a slope is positive?

Back

A positive slope indicates that as x increases, y also increases. The line slopes upward from left to right.

Tags

CCSS.8.EE.B.5

Front

How can you compare the costs of two services represented by linear equations?

Back

To compare costs, evaluate both equations at the same value of x (number of services) and compare the resulting y values (total costs).

Tags

CCSS.8.EE.C.8C

Front

What is the formula for calculating the total cost of a service with a fixed fee and a variable fee?

Back

The total cost can be calculated using the formula y = mx + b, where m is the variable cost per unit, x is the number of units, and b is the fixed fee.

Tags

CCSS.8.EE.B.5

Front

What does the initial fee in a service cost equation represent?

Back

The initial fee represents the fixed cost that must be paid regardless of the number of services used.

Tags

CCSS.HSF.LE.B.5