5.1 Linear Functions

Answer explanation

-23x + y = 16

ADD 23x to both sides

y = 16 + 23x

Tags

CCSS.6.EE.C.9

Answer explanation

4x + 2y = 120

-4x -4x

2y = 120 - 4x

divide both sides (ALL TERMS) by 2

y = 60 - 2x

Tags

CCSS.6.EE.C.9

Tags

CCSS.6.EE.C.9

What is the definition of function?

• Has inputs and outputs

• Every input has only ONE output

• x-values and y-values

• Inputs have different outputs every time

Answer explanation

We must know where an input will go in the output!

Tags

CCSS.8.F.A.1

Does the graph represent a linear function, a non-linear function, or is it not a function?

• not a function

• linear function

• non-linear function

Answer explanation

All straight lines, except vertical lines, are linear functions! They will pass the vertical line test, and have a constant rate of change.

Tags

CCSS.8.F.A.3

Does the graph represent a linear function, a non-linear function, or is it not a function?

• not a function

• linear function

• non-linear function

Answer explanation

This is a function, but it does not have a constant slope. It is not a straight line!

Tags

CCSS.8.F.A.3

Does the table represent a linear function, a non-linear function, or is it not a function?

• not a function

• Non-linear function

• Linear function

Answer explanation

As x increases by 1, the y value increases by 3. This is true for all x and y

Tags

CCSS.8.F.A.3

Does the table represent a linear function, a non-linear function, or is it not a function?

• Linear Function

• Non-linear Function

• Not a Function

Answer explanation

Did you notice what happens at Time = 3?

We have TWO outputs for ONE input! Not good!

Tags

CCSS.8.F.A.3

• Linear Function

• Non-Linear Function

• Not a Function

Answer explanation

A linear function CAN be written in standard form Ax + By = C. It does not have to be.

In this case, we subtract 23y from both sides and now we have a standard form equation -5x - 5y = 6

Tags

CCSS.8.F.A.3

• Linear Function

• Non-linear function

• Not a function

Answer explanation

The graph of y=4 will be a HORIZONTAL line, which is a function!

Written in the standard form, this is 0x + 1y = 4

Tags

CCSS.8.F.A.3