Fill In The Table Using This Function Rule: Y = − 2 X + 5 Y = -2x + 5 Y = − 2 X + 5 \[ \begin{tabular}{|c|c|} \hline X$ & Y Y Y \ \hline -4 & □ \square □ \ \hline -2 & □ \square □ \ \hline 0 & □ \square □ \ \hline 2 & □ \square □

Introduction

In mathematics, linear equations are a fundamental concept that helps us understand the relationship between variables. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on solving linear equations using a function rule, specifically the equation $y = -2x + 5$. We will use this equation to fill in a table with missing values.

Understanding the Function Rule

The function rule $y = -2x + 5$ is a linear equation that describes a straight line. The equation is in the slope-intercept form, where $y$ is the dependent variable, $x$ is the independent variable, and $-2$ is the slope of the line. The slope represents the rate of change of the line, and the $+5$ is the y-intercept, which is the point where the line intersects the y-axis.

Filling in the Table

To fill in the table, we will substitute the given values of $x$ into the function rule and solve for $y$. The table is as follows:

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

Step 1: Substituting x = -4

To find the value of $y$ when $x = -4$, we substitute $-4$ into the function rule:

$y = -2(-4) + 5$

Using the order of operations, we first multiply $-2$ and $-4$:

$y = 8 + 5$

Then, we add $8$ and $5$:

$y = 13$

So, the value of $y$ when $x = -4$ is $13$.

Step 2: Substituting x = -2

To find the value of $y$ when $x = -2$, we substitute $-2$ into the function rule:

$y = -2(-2) + 5$

Using the order of operations, we first multiply $-2$ and $-2$:

$y = 4 + 5$

Then, we add $4$ and $5$:

$y = 9$

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

Step 3: Substituting x = 0

To find the value of $y$ when $x = 0$, we substitute $0$ into the function rule:

$y = -2(0) + 5$

Using the order of operations, we first multiply $-2$ and $0$:

$y = 0 + 5$

Then, we add $0$ and $5$:

$y = 5$

So, the value of $y$ when $x = 0$ is $5$.

Step 4: Substituting x = 2

To find the value of $y$ when $x = 2$, we substitute $2$ into the function rule:

$y = -2(2) + 5$

Using the order of operations, we first multiply $-2$ and $2$:

$y = -4 + 5$

Then, we add $-4$ and $5$:

$y = 1$

So, the value of $y$ when $x = 2$ is $1$.

Conclusion

In this article, we used the function rule $y = -2x + 5$ to fill in a table with missing values. We substituted the given values of $x$ into the function rule and solved for $y$. The resulting table is as follows:

$x$	$y$
-4	13
-2	9
0	5
2	1

This exercise demonstrates the importance of understanding linear equations and how to use them to solve problems. By following the function rule, we can easily fill in the table with the correct values.

Discussion

• What is the slope of the line represented by the function rule $y = -2x + 5$?
• What is the y-intercept of the line represented by the function rule $y = -2x + 5$?
• How can you use the function rule to find the value of $y$ when $x = 3$?
• What is the relationship between the values of $x$ and $y$ in the table?

Answer Key

• The slope of the line represented by the function rule $y = -2x + 5$ is $-2$.
• The y-intercept of the line represented by the function rule $y = -2x + 5$ is $5$.
• To find the value of $y$ when $x = 3$, we substitute $3$ into the function rule: $y = -2(3) + 5 = -6 + 5 = -1$.
• The relationship between the values of $x$ and $y$ in the table is a linear relationship, where $y$ decreases as $x$ increases.
  Frequently Asked Questions: Linear Equations and Function Rules ====================================================================

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: What is a function rule?

A: A function rule is a mathematical equation that describes a relationship between two variables. It is used to find the value of one variable when the other variable is known.

Q: How do I write a function rule in slope-intercept form?

A: To write a function rule in slope-intercept form, you need to identify the slope and the y-intercept. The slope is the rate of change of the line, and the y-intercept is the point where the line intersects the y-axis. The function rule is written in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: How do I find the slope of a line?

A: To find the slope of a line, you need to use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.

Q: How do I find the y-intercept of a line?

A: To find the y-intercept of a line, you need to use the formula $b = y_1 - mx_1$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope.

Q: How do I use a function rule to solve a problem?

A: To use a function rule to solve a problem, you need to substitute the given values into the function rule and solve for the unknown variable.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2.

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to use a coordinate plane and plot two points on the line. Then, draw a line through the two points to represent the linear equation.

Q: What is the relationship between the values of x and y in a linear equation?

A: In a linear equation, the values of x and y are related by a straight line. As x increases, y increases or decreases at a constant rate.

Q: Can I use a function rule to solve a problem with multiple variables?

A: Yes, you can use a function rule to solve a problem with multiple variables. However, you need to make sure that the function rule is written in a way that takes into account all the variables.

Q: How do I determine if a function rule is linear or non-linear?

A: To determine if a function rule is linear or non-linear, you need to look at the highest power of the variable(s). If the highest power is 1, the function rule is linear. If the highest power is greater than 1, the function rule is non-linear.

Q: What are some real-world applications of linear equations and function rules?

A: Linear equations and function rules have many real-world applications, including:

• Modeling population growth
• Calculating the cost of goods
• Determining the trajectory of an object
• Solving problems in physics and engineering

Conclusion

In this article, we have answered some frequently asked questions about linear equations and function rules. We have covered topics such as writing a function rule in slope-intercept form, finding the slope and y-intercept of a line, and using a function rule to solve a problem. We have also discussed the relationship between the values of x and y in a linear equation and the difference between a linear equation and a quadratic equation.