Key Features of 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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.EE.B.5

Front

How do you find the x-intercept of a linear function?

Back

To find the x-intercept, set y = 0 in the equation of the line and solve for x.

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 is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Tags

CCSS.8.EE.B.5

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Tags

CCSS.8.EE.B.5

Front

How can you determine if a linear function is increasing or decreasing?

Back

If the slope is positive, the function is increasing; if the slope is negative, the function is decreasing.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the average rate of change in a linear function?

Back

The average rate of change is the slope of the line, representing how much y changes for a unit change in x.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

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

Back

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

Tags

CCSS.8.EE.B.5