Fill In The Table Using The Function Rule $y = -3x + 3$.$\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline -4 & $\square$ \\ \hline -2 & $\square$ \\ \hline 0 & $\square$ \\ \hline 2 & $\square$

Solving Linear Equations: Filling in the Table Using the Function Rule

In mathematics, a function rule is a mathematical expression that describes the relationship between the input and output values of a function. The function rule $y = -3x + 3$ is a linear equation that represents a straight line on a coordinate plane. In this article, we will use this function rule to fill in a table with missing values.

Understanding the Function Rule

The function rule $y = -3x + 3$ is a linear equation that can be written in the slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In this case, the slope is $-3$ and the y-intercept is $3$. This means that for every unit increase in $x$, the value of $y$ decreases by $3$ units.

Filling in the Table

To fill in the table, we need to substitute the given values of $x$ into the function rule and calculate the corresponding values of $y$. Let's start by filling in the table with the given values of $x$.

$x$	$y$
-4	$\square$
-2	$\square$
0	$\square$
2	$\square$

Step 1: Filling in the Value of $y$ for $x = -4$

To fill in the value of $y$ for $x = -4$, we substitute $x = -4$ into the function rule:

$$y = -3(-4) + 3$$

Simplifying the equation, we get:

$$y = 12 + 3$$

$$y = 15$$

So, the value of $y$ for $x = -4$ is $15$.

$x$	$y$
-4	15
-2	$\square$
0	$\square$
2	$\square$

Step 2: Filling in the Value of $y$ for $x = -2$

To fill in the value of $y$ for $x = -2$, we substitute $x = -2$ into the function rule:

$$y = -3(-2) + 3$$

Simplifying the equation, we get:

$$y = 6 + 3$$

$$y = 9$$

So, the value of $y$ for $x = -2$ is $9$.

$x$	$y$
-4	15
-2	9
0	$\square$
2	$\square$

Step 3: Filling in the Value of $y$ for $x = 0$

To fill in the value of $y$ for $x = 0$, we substitute $x = 0$ into the function rule:

$$y = -3(0) + 3$$

Simplifying the equation, we get:

$$y = 0 + 3$$

$$y = 3$$

So, the value of $y$ for $x = 0$ is $3$.

$x$	$y$
-4	15
-2	9
0	3
2	$\square$

Step 4: Filling in the Value of $y$ for $x = 2$

To fill in the value of $y$ for $x = 2$, we substitute $x = 2$ into the function rule:

$$y = -3(2) + 3$$

Simplifying the equation, we get:

$$y = -6 + 3$$

$$y = -3$$

So, the value of $y$ for $x = 2$ is $-3$.

$x$	$y$
-4	15
-2	9
0	3
2	-3

In this article, we used the function rule $y = -3x + 3$ to fill in a table with missing values. We substituted the given values of $x$ into the function rule and calculated the corresponding values of $y$. The resulting table shows the relationship between the input and output values of the function.

The final answer is:

$x$	$y$
-4	15
-2	9
0	3
2	-3

Frequently Asked Questions (FAQs) About Filling in the Table Using the Function Rule

In the previous article, we used the function rule $y = -3x + 3$ to fill in a table with missing values. In this article, we will answer some frequently asked questions (FAQs) about filling in the table using the function rule.

Q: What is the function rule?

A: The function rule is a mathematical expression that describes the relationship between the input and output values of a function. In this case, the function rule is $y = -3x + 3$.

Q: What is the slope-intercept form of a linear equation?

A: The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: What is the slope of the function rule?

A: The slope of the function rule is $-3$. This means that for every unit increase in $x$, the value of $y$ decreases by $3$ units.

Q: What is the y-intercept of the function rule?

A: The y-intercept of the function rule is $3$. This means that when $x = 0$, the value of $y$ is $3$.

Q: How do I fill in the table using the function rule?

A: To fill in the table using the function rule, you need to substitute the given values of $x$ into the function rule and calculate the corresponding values of $y$.

Q: What if I have a negative value of $x$?

A: If you have a negative value of $x$, you can still use the function rule to fill in the table. For example, if $x = -4$, you can substitute $x = -4$ into the function rule to get $y = -3(-4) + 3 = 15$.

Q: What if I have a fractional value of $x$?

A: If you have a fractional value of $x$, you can still use the function rule to fill in the table. For example, if $x = -\frac{1}{2}$, you can substitute $x = -\frac{1}{2}$ into the function rule to get $y = -3(-\frac{1}{2}) + 3 = \frac{9}{2}$.

Q: Can I use the function rule to fill in a table with multiple values of $x$?

A: Yes, you can use the function rule to fill in a table with multiple values of $x$. For example, if you have a table with values of $x$ ranging from $-4$ to $4$, you can use the function rule to fill in the table.

Q: What if I make a mistake when filling in the table?

A: If you make a mistake when filling in the table, you can always go back and recheck your work. You can also use a calculator or a computer program to help you fill in the table.

In this article, we answered some frequently asked questions (FAQs) about filling in the table using the function rule. We hope that this article has been helpful in answering your questions and providing you with a better understanding of the function rule.

The final answer is:

$x$	$y$
-4	15
-2	9
0	3
2	-3

Note: The final answer is the same as in the previous article.