Evaluating Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Front

How do you evaluate a linear function at a specific point?

Back

To evaluate a linear function at a specific point, substitute the value of x into the function and simplify to find f(x).

Tags

CCSS.HSF.IF.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

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the value of y when x = 0; it is the point where the line crosses the y-axis.

Front

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

Back

To find the x-intercept of a linear function, set f(x) = 0 and solve for x.

Front

What is the significance of the equation f(x) = mx + b?

Back

The equation f(x) = mx + b represents a straight line in a Cartesian plane, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

How do you solve for x in the equation y = mx + b?

Back

To solve for x in the equation y = mx + b, rearrange the equation to x = (y - b) / m.

Tags

CCSS.HSA.CED.A.4

Front

What does it mean if a linear function has a negative slope?

Back

If a linear function has a negative slope, it means that as x increases, y decreases, indicating an inverse relationship between x and y.

Tags

CCSS.8.EE.B.5

Front

How do you determine if a point lies on the graph of a linear function?

Back

To determine if a point (x, y) lies on the graph of a linear function, substitute x into the function and check if the resulting f(x) equals y.

Tags

CCSS.HSF.IF.A.2

Front

What is the process for graphing a linear function?

Back

To graph a linear function, identify the y-intercept, use the slope to find another point, and draw a straight line through the points.