Fill In The Table Using This Function Rule: $y = 5x - 7$\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 2 & $\square$ \\ \hline 5 & $\square$ \\ \hline 7 & $\square$ \\ \hline 8 & $\square$

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

In mathematics, linear equations are a fundamental concept that helps us understand the relationship between two 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 the function rule, specifically the equation $y = 5x - 7$. We will use this equation to fill in a table with missing values.

Understanding the Function Rule

The function rule $y = 5x - 7$ tells us that for every value of $x$, there is a corresponding value of $y$. The equation is in the form of $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In this case, the slope is 5 and the y-intercept is -7.

Filling in the Table

To fill in the table, we need to substitute the given values of $x$ into the function rule and solve for $y$.

Substituting $x = 2$

When $x = 2$, we substitute this value into the function rule:

$y = 5(2) - 7$

Using the order of operations, we first multiply 5 and 2:

$y = 10 - 7$

Then, we subtract 7 from 10:

$y = 3$

So, when $x = 2$, $y = 3$.

Substituting $x = 5$

When $x = 5$, we substitute this value into the function rule:

$y = 5(5) - 7$

Using the order of operations, we first multiply 5 and 5:

$y = 25 - 7$

Then, we subtract 7 from 25:

$y = 18$

So, when $x = 5$, $y = 18$.

Substituting $x = 7$

When $x = 7$, we substitute this value into the function rule:

$y = 5(7) - 7$

Using the order of operations, we first multiply 5 and 7:

$y = 35 - 7$

Then, we subtract 7 from 35:

$y = 28$

So, when $x = 7$, $y = 28$.

Substituting $x = 8$

When $x = 8$, we substitute this value into the function rule:

$y = 5(8) - 7$

Using the order of operations, we first multiply 5 and 8:

$y = 40 - 7$

Then, we subtract 7 from 40:

$y = 33$

So, when $x = 8$, $y = 33$.

In this article, we used the function rule $y = 5x - 7$ to fill in a table with missing values. We substituted the given values of $x$ into the function rule and solved for $y$. By following the order of operations, we were able to find the corresponding values of $y$ for each value of $x$. This demonstrates the importance of understanding linear equations and how to apply them to real-world problems.

$x$	$y$
2	3
5	18
7	28
8	33

• What is the slope of the function rule $y = 5x - 7$?
• What is the y-intercept of the function rule $y = 5x - 7$?
• How do you fill in a table using a function rule?
• What is the relationship between the values of $x$ and $y$ in the function rule $y = 5x - 7$?

• The slope of the function rule $y = 5x - 7$ is 5.
• The y-intercept of the function rule $y = 5x - 7$ is -7.
• To fill in a table using a function rule, substitute the given values of $x$ into the function rule and solve for $y$.
• The relationship between the values of $x$ and $y$ in the function rule $y = 5x - 7$ is a linear relationship, where $y$ increases by 5 units for every 1 unit increase in $x$.
  Frequently Asked Questions (FAQs) About 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 is a simple equation that can be graphed as a straight line.

Q: What is a function rule?

A: A function rule is an equation that describes the relationship between two variables, typically represented as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: How do I find the slope of a function rule?

A: To find the slope of a function rule, look for the coefficient of the variable (usually $x$) in the equation. The slope is the number that is multiplied by the variable.

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

A: To find the y-intercept of a function rule, look for the constant term in the equation. The y-intercept is the value of $y$ when $x = 0$.

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

A: To fill in a table using a function rule, substitute the given values of $x$ into the function rule and solve for $y$.

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. For every 1 unit increase in $x$, $y$ increases by the slope (m) units.

Q: How do I graph a linear equation?

A: To graph a linear equation, plot two points on the graph using the function rule. The first point is the y-intercept, and the second point is a point on the line. Draw a straight line through the two points to graph the equation.

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 solve a linear equation?

A: To solve a linear equation, isolate the variable (usually $x$) on one side of the equation. Use inverse operations to get rid of any constants or coefficients that are being added or subtracted from the variable.

Q: What is the significance of linear equations in real-world problems?

A: Linear equations are used to model real-world problems, such as the cost of goods, the distance traveled by an object, and the amount of money earned by an individual.

Q: How do I use linear equations to solve problems in science and engineering?

A: Linear equations are used to model real-world problems in science and engineering, such as the motion of objects, the flow of fluids, and the behavior of electrical circuits.

Q: What are some common applications of linear equations?

A: Some common applications of linear equations include:

• Cost-benefit analysis
• Distance-time problems
• Money earned or spent
• Motion of objects
• Electrical circuits
• Fluid flow

In this article, we have answered some frequently asked questions about linear equations and function rules. We have discussed the definition of linear equations, function rules, and how to fill in a table using a function rule. We have also covered the relationship between the values of $x$ and $y$ in a linear equation and how to graph a linear equation. Additionally, we have discussed the significance of linear equations in real-world problems and some common applications of linear equations.