### Student Page2.8.4Distinguishing Linear from Other Functions A4US

#### 1.

What do you know about linear equations? Give brief answers now and think about these questions as you work on the problems below.

##### (a)

What patterns would you see in a table of data that can be modeled by a linear equation?

##### (b)

How can you tell a graph can be modeled by a linear equation?

##### (c)

What does an equation of a linear equation look like?

##### (d)

How can you tell a story can be modeled by a linear equation?

#### 2.

Study the data sets. Label each data set as linear or non-linear. Explain your choice.

##### (a)
$$x$$ $$y$$
$$-5$$ $$-14$$
$$-4$$ $$-12$$
$$-3$$ $$-10$$
$$-2$$ $$-8$$
$$-1$$ $$-6$$
0 $$-4$$
1 $$-2$$
2 0
3 2
4 4
5 6

Linear / Non-linear? Explain:

##### (b)
$$x$$ $$y$$
$$-5$$ 0.03125
$$-4$$ 0.0625
$$-3$$ 0.125
$$-2$$ 0.25
$$-1$$ 0.5
0 1
1 2
2 4
3 8
4 16
5 32

Linear / Non-linear? Explain:

##### (c)
$$x$$ $$y$$
$$-5$$ 25
$$-4$$ 16
$$-3$$ 9
$$-2$$ 4
$$-1$$ 1
0 0
1 1
2 4
3 9
4 16
5 25

Linear / Non-linear? Explain:

#### 3.

Categorize each graph as linear or non-linear. Explain your choice.

##### (a) Linear / Non-linear? Explain:

##### (b) Linear / Non-linear? Explain:

##### (c) Linear / Non-linear? Explain:

#### 4.

Gather data for each story. Label each data set as linear or non-linear. Explain your choice.

##### (a)

Geppetto carved Pinocchio a 2-inch long nose. Each time Pinocchio tells a lie, his nose grows 3 inches. How long will his nose be after 1 lie? 2 lies? 3 lies? $$L$$ lies?

Lie Number Nose Length in inches
0 2
1
2
3
4
5
$$L$$

Linear / Non-linear? Explain:

##### (b)

Geppetto carved Pinocchio a 2-inch long nose. Each time Pinocchio tells a lie, his nose doubles in length. How long will his nose be after 1 lie? 2 lies? 3 lies? $$L$$ lies?

Lie Number Nose Length in inches
0 2
1
2
3
4
5
$$L$$

Linear / Non-linear? Explain:

##### (c)

Geppetto carved Pinocchio a 2-inch long nose. Each time Pinocchio tells a lie, his nose grows from its previous length by the same number of inches as the number of lies he has told. For example, after 1 lie, his nose will be 2 + 1 = 3 inches long. After 2 lies, his nose will be 3 + 2 = 5 inches long. How long will his nose be after 3 lies? 4 lies? 5 lies? $$L$$ lies?

Lie Number Nose Length in inches
0 2
1 3
2 5
3
4
5
$$L$$

Linear / Non-linear? Explain:

#### 5.

Categorize each equation as linear or non-linear. Explain your choice.

##### (a)

$$y = 3x + 4$$

Linear / Non-linear? Explain:

##### (b)

$$y = 2^x + 3$$

Linear / Non-linear? Explain:

##### (c)

$$y = x^2 + 1$$

Linear / Non-linear? Explain:

#### 6.

##### (a)

What patterns would you see in a table that can be modeled by a linear equation?

##### (b)

How can you tell a graph can be modeled by a linear equation?

##### (c)

What does an equation of a linear equation look like?

##### (d)

How can you tell a story can be modeled by a linear equation?