### All Common Core: 8th Grade Math Resources

## Example Questions

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

Select the equation that best represents a linear function.

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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:

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.

**Possible Answers:**

**Correct answer:**

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:

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.

**Possible Answers:**

**Correct answer:**

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:

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.

**Possible Answers:**

**Correct answer:**

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:

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 ?

**Possible Answers:**

**Correct answer:**

Start by visualizing the graph associated with the function :

Terms within the parentheses associated with the squared x-variable will shift the parabola horizontally, while terms outside of the parentheses will shift the parabola vertically. In the provided equation, 2 is located outside of the parentheses and is subtracted from the terms located within the parentheses; therefore, the parabola in the graph will shift down by 2 units. A simplified graph of looks like this:

Remember that there is also a term within the parentheses. Within the parentheses, 1 is subtracted from the x-variable; thus, the parabola in the graph will shift to the right by 1 unit. As a result, the following graph matches the given function :