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.8.F.B.4

CCSS.HSF.LE.A.2

Front

How do you find the value of a linear function at a specific point?

Back

To find the value of a linear function f(x) at a specific point x = a, substitute a into the function: f(a).

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 f(x) when x = 0; it is the point where the line crosses the y-axis.

Front

How do you solve for x in a linear equation?

Back

To solve for x in a linear equation, isolate x on one side of the equation using algebraic operations.

Tags

CCSS.7.EE.B.4A

Front

What is the significance of the equation w(x) = 3x - 7?

Back

This equation represents a linear function where the slope is 3 and the y-intercept is -7.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

How do you evaluate a linear function at a negative input?

Back

To evaluate a linear function at a negative input, substitute the negative value into the function and simplify.

Tags

CCSS.HSF.IF.A.2

Front

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

Back

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

Tags

CCSS.8.EE.B.5

Front

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

Back

To determine if a point (a, b) lies on the graph of a linear function, substitute a into the function and check if f(a) = b.

Tags

CCSS.HSF.IF.A.2

Front

What is the process to graph 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.