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 (m) represent in a linear function?

Back

The slope (m) 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

What is the y-intercept (b) in a linear function?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you identify the slope from the equation y = 4x + 2?

Back

The slope is 4, which means for every 1 unit increase in x, y increases by 4 units.

Tags

CCSS.8.EE.B.5

Front

What is the equation of a linear function with a slope of 2 and a y-intercept of 5?

Back

The equation is y = 2x + 5.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

If a linear function has a slope of -3, what does this indicate about the graph?

Back

A slope of -3 indicates that the graph of the function decreases as x increases, meaning y decreases by 3 units for every 1 unit increase in x.

Tags

CCSS.8.EE.B.5

Front

How do you write the equation of a line given a slope of 1 and a y-intercept of -4?

Back

The equation is y = 1x - 4 or simply y = x - 4.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

What is the change in y when x changes from 1 to 2 in the function y = 3x + 1?

Back

The change in y is 3, as y changes from 10 to 13.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

How do you find the starting value of a linear function?

Back

The starting value is found by evaluating the function at x = 0, which gives the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does it mean if a linear function has a slope of 0?

Back

A slope of 0 means the function is constant; the graph is a horizontal line.

Tags

CCSS.8.EE.B.5