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.

We can add to both sides:

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

From the vertex, we know that the equation of the parabola will take the form for some .

To calculate that , we plug in the values from the other point we are given, , and solve for :

Now the equation is . This is not an answer choice, so we need to rewrite it in some way.

Expand the squared term:

Distribute the fraction through the parentheses:

Combine like terms:

Starting with

moves the parabola by units to the right.

Similarly moves the parabola by units to the left.

Hence the correct answer is option .

From the vertex, we know that the equation of the parabola will take the form for some .

To calculate that , we plug in the values from the other point we are given, , and solve for :

Now the equation is . This is not an answer choice, so we need to rewrite it in some way.

Expand the squared term:

Distribute the fraction through the parentheses:

Combine like terms:

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.

We can add to both sides:

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

We can add to both sides:

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

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.

Starting with

moves the parabola by units to the right.

Similarly moves the parabola by units to the left.

Hence the correct answer is option .