# Common Core: 8th Grade Math : Understand Linear and Nonlinear Functions: CCSS.Math.Content.8.F.A.3

## Example Questions

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### Example Question #11 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Select the equation that best represents a linear function.

Explanation:

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our  value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

Again, though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

For this equation, we can solve for  to make sure this equation can be written is slope-intercept form. From first glance it looks to be correct because none of our variables are written to a power. In order to tell for certain, we need to isolate the y variable on the left side of the equation.

First, we can subtract  from both sides:

Next, we can divide each side by

This equation is in slope-intercept form; thus,  is the correct answer.

### Example Question #11 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Select the equation that best represents a linear function.

Explanation:

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our  value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

Again, though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

For this equation, we can solve for  to make sure this equation can be written is slope-intercept form. From first glance it looks to be correct because none of our variables are written to a power. In order to tell for certain, we need to isolate the y variable on the left side of the equation.

First, we can subtract  from both sides:

This equation is in slope-intercept form; thus,  is the correct answer.

### Example Question #41 : Functions

Select the equation that best represents a linear function.

Explanation:

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our  value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

Again, though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

For this equation, we can solve for  to make sure this equation can be written is slope-intercept form. From first glance it looks to be correct because none of our variables are written to a power. In order to tell for certain, we need to isolate the y variable on the left side of the equation.

First, we can subtract  from both sides:

Next, we can divide each side by

This equation is in slope-intercept form; thus,  is the correct answer.

### Example Question #41 : Functions

Select the equation that best represents a linear function.

Explanation:

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our  value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

Again, though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

For this equation, we can solve for  to make sure this equation can be written is slope-intercept form. From first glance it looks to be correct because none of our variables are written to a power. In order to tell for certain, we need to isolate the y variable on the left side of the equation.

First, we can subtract  from both sides:

This equation is in slope-intercept form; thus,  is the correct answer.

### Example Question #301 : Grade 8

Select the equation that best represents a linear function.

Explanation:

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our  value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

Again, though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

This equation is in slope-intercept form; thus,  is the correct answer.

### Example Question #42 : Functions

Select the equation that best represents a linear function.

Explanation:

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our  value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

Again, though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

For this equation, we can solve for  to make sure this equation can be written is slope-intercept form. From first glance it looks to be correct because none of our variables are written to a power. In order to tell for certain, we need to isolate the y variable on the left side of the equation.

First, we can subtract  from both sides:

This equation is in slope-intercept form; thus,  is the correct answer.

### Example Question #11 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Select the equation that best represents a linear function.

Explanation:

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear.

Let's take a look at our answer choices:

Notice that in this equation our  value is to the third power, which does not match our slope-intercept form.

Though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

Again, though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power.

This equation is in slope-intercept form; thus,  is the correct answer.

### Example Question #1 : How To Graph A Quadratic Function

Which of the following graphs matches the function ?