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 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).

Tags

CCSS.8.EE.B.5

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

If a line has a slope of -1, what does this indicate about its direction?

Back

A slope of -1 indicates that the line descends from left to right, meaning as x increases, y decreases.

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line represented by the equation y = 2x + 4?

Back

The slope of the line is 2.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of the line represented by the equation y = -3x + 1?

Back

The y-intercept of the line is 1.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in y as x changes.

Tags

CCSS.8.EE.B.5

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it does not change in x as y changes.

Tags

CCSS.8.EE.B.5

Front

How can you identify the slope and y-intercept from the equation y = mx + b?

Back

In the equation y = mx + b, m represents the slope and b represents the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3