How to Select Ordered Pairs

Oct 13, 2025 by wbrum.org 118 views

In a Verbal Representation, a Function is Described as a Number $y$ which is 6 Less than the Product of Numbers 2 and $x$

Understanding the Problem

In this problem, we are given a verbal representation of a function, which describes the relationship between two variables, $x$ and $y$ . The function is defined as a number $y$ that is 6 less than the product of numbers 2 and $x$ . This can be represented mathematically as $y = 2x - 6$ . Our task is to select all sets of ordered pairs that represent the given function.

What are Ordered Pairs?

Ordered pairs are a way to represent the relationship between two variables, $x$ and $y$ , in a mathematical function. An ordered pair is a pair of values, $(x, y)$ , where $x$ is the input value and $y$ is the output value. For example, if we have an ordered pair $(2, 4)$ , it means that when the input value is 2, the output value is 4.

How to Select Ordered Pairs

To select the ordered pairs that represent the given function, we need to substitute different values of $x$ into the equation $y = 2x - 6$ and find the corresponding values of $y$ . This will give us a set of ordered pairs that satisfy the equation.

Step 1: Substitute $x = 0$

Let's start by substituting $x = 0$ into the equation $y = 2x - 6$ . This gives us:

$y = 2(0) - 6$ $y = -6$

So, when $x = 0$ , the corresponding value of $y$ is $-6$ . This gives us our first ordered pair: $(0, -6)$ .

Step 2: Substitute $x = 1$

Next, let's substitute $x = 1$ into the equation $y = 2x - 6$ . This gives us:

$y = 2(1) - 6$ $y = -4$

So, when $x = 1$ , the corresponding value of $y$ is $-4$ . This gives us our second ordered pair: $(1, -4)$ .

Step 3: Substitute $x = 2$

Now, let's substitute $x = 2$ into the equation $y = 2x - 6$ . This gives us:

$y = 2(2) - 6$ $y = -2$

So, when $x = 2$ , the corresponding value of $y$ is $-2$ . This gives us our third ordered pair: $(2, -2)$ .

Step 4: Substitute $x = 3$

Next, let's substitute $x = 3$ into the equation $y = 2x - 6$ . This gives us:

$y = 2(3) - 6$ $y = 0$

So, when $x = 3$ , the corresponding value of $y$ is $0$ . This gives us our fourth ordered pair: $(3, 0)$ .

Step 5: Substitute $x = 4$

Now, let's substitute $x = 4$ into the equation $y = 2x - 6$ . This gives us:

$y = 2(4) - 6$ $y = 2$

So, when $x = 4$ , the corresponding value of $y$ is $2$ . This gives us our fifth ordered pair: $(4, 2)$ .

Step 6: Substitute $x = 5$

Finally, let's substitute $x = 5$ into the equation $y = 2x - 6$ . This gives us:

$y = 2(5) - 6$ $y = 4$

So, when $x = 5$ , the corresponding value of $y$ is $4$ . This gives us our sixth ordered pair: $(5, 4)$ .

Conclusion

In this problem, we were given a verbal representation of a function, which described the relationship between two variables, $x$ and $y$ . We were asked to select all sets of ordered pairs that represent the given function. To do this, we substituted different values of $x$ into the equation $y = 2x - 6$ and found the corresponding values of $y$ . This gave us a set of ordered pairs that satisfy the equation. The ordered pairs that represent the given function are:

$(0, -6)$
$(1, -4)$
$(2, -2)$
$(3, 0)$
$(4, 2)$
$(5, 4)$

What's Next?

Now that we have found the ordered pairs that represent the given function, we can use this information to graph the function. We can plot the ordered pairs on a coordinate plane and draw a line through them to represent the function. This will give us a visual representation of the function and help us understand its behavior.

Graphing the Function

To graph the function, we can start by plotting the ordered pairs on a coordinate plane. We can use a ruler to draw a line through the points to represent the function. As we can see from the graph, the function is a linear function that has a slope of 2 and a y-intercept of -6.

Interpreting the Graph

The graph of the function shows us that the function is a linear function that has a slope of 2 and a y-intercept of -6. This means that for every 1 unit increase in the input value $x$ , the output value $y$ increases by 2 units. The y-intercept of -6 means that when the input value $x$ is 0, the output value $y$ is -6.

Real-World Applications

The function $y = 2x - 6$ has many real-world applications. For example, it can be used to model the cost of producing a product, where the input value $x$ represents the number of units produced and the output value $y$ represents the total cost. It can also be used to model the revenue of a business, where the input value $x$ represents the number of units sold and the output value $y$ represents the total revenue.

Conclusion

$(0, -6)$
$(1, -4)$
$(2, -2)$
$(3, 0)$
$(4, 2)$
$(5, 4)$

We also graphed the function and interpreted the graph to understand its behavior. The function has many real-world applications, including modeling the cost of producing a product and the revenue of a business.
Q&A: Understanding the Function $y = 2x - 6$

Q: What is the function $y = 2x - 6$ ?

A: The function $y = 2x - 6$ is a linear function that describes the relationship between two variables, $x$ and $y$ . It is defined as a number $y$ that is 6 less than the product of numbers 2 and $x$ .

Q: How do I graph the function $y = 2x - 6$ ?

A: To graph the function $y = 2x - 6$ , you can start by plotting the ordered pairs on a coordinate plane. You can use a ruler to draw a line through the points to represent the function. As you can see from the graph, the function is a linear function that has a slope of 2 and a y-intercept of -6.

Q: What is the slope of the function $y = 2x - 6$ ?

A: The slope of the function $y = 2x - 6$ is 2. This means that for every 1 unit increase in the input value $x$ , the output value $y$ increases by 2 units.

Q: What is the y-intercept of the function $y = 2x - 6$ ?

A: The y-intercept of the function $y = 2x - 6$ is -6. This means that when the input value $x$ is 0, the output value $y$ is -6.

Q: How do I use the function $y = 2x - 6$ in real-world applications?

A: The function $y = 2x - 6$ has many real-world applications. For example, it can be used to model the cost of producing a product, where the input value $x$ represents the number of units produced and the output value $y$ represents the total cost. It can also be used to model the revenue of a business, where the input value $x$ represents the number of units sold and the output value $y$ represents the total revenue.

Q: Can I use the function $y = 2x - 6$ to model a non-linear relationship?

A: No, the function $y = 2x - 6$ is a linear function and can only be used to model linear relationships. If you need to model a non-linear relationship, you will need to use a different type of function, such as a quadratic or exponential function.

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

A: To determine if a function is linear or non-linear, you can look at its graph. If the graph is a straight line, the function is linear. If the graph is a curve, the function is non-linear.

Q: Can I use the function $y = 2x - 6$ to model a relationship between two variables that are not linearly related?

A: No, the function $y = 2x - 6$ is a linear function and can only be used to model linear relationships. If the relationship between the two variables is not linear, you will need to use a different type of function, such as a quadratic or exponential function.

Q: How do I choose the correct function to model a real-world relationship?

A: To choose the correct function to model a real-world relationship, you need to consider the nature of the relationship between the two variables. If the relationship is linear, you can use a linear function. If the relationship is non-linear, you will need to use a different type of function, such as a quadratic or exponential function.

Q: Can I use the function $y = 2x - 6$ to model a relationship between two variables that have different units?

A: No, the function $y = 2x - 6$ is a linear function and can only be used to model relationships between variables that have the same units. If the variables have different units, you will need to use a different type of function, such as a conversion factor or a unit conversion function.

Q: How do I convert between different units when modeling a real-world relationship?

A: To convert between different units when modeling a real-world relationship, you can use a conversion factor or a unit conversion function. This will allow you to express the relationship between the variables in terms of the same units.

Q: Can I use the function $y = 2x - 6$ to model a relationship between two variables that are not directly related?

A: No, the function $y = 2x - 6$ is a linear function and can only be used to model direct relationships between variables. If the variables are not directly related, you will need to use a different type of function, such as a quadratic or exponential function.

Q: How do I determine if a relationship between two variables is direct or indirect?

A: To determine if a relationship between two variables is direct or indirect, you need to consider the nature of the relationship. If the relationship is direct, you can use a linear function. If the relationship is indirect, you will need to use a different type of function, such as a quadratic or exponential function.

Q: Can I use the function $y = 2x - 6$ to model a relationship between two variables that have different scales?

A: No, the function $y = 2x - 6$ is a linear function and can only be used to model relationships between variables that have the same scale. If the variables have different scales, you will need to use a different type of function, such as a scaling function or a normalization function.

Q: How do I scale or normalize a function to model a relationship between variables with different scales?

A: To scale or normalize a function to model a relationship between variables with different scales, you can use a scaling function or a normalization function. This will allow you to express the relationship between the variables in terms of the same scale.

Q: Can I use the function $y = 2x - 6$ to model a relationship between two variables that are not independent?

A: No, the function $y = 2x - 6$ is a linear function and can only be used to model independent relationships between variables. If the variables are not independent, you will need to use a different type of function, such as a quadratic or exponential function.

Q: How do I determine if a relationship between two variables is independent or dependent?

A: To determine if a relationship between two variables is independent or dependent, you need to consider the nature of the relationship. If the relationship is independent, you can use a linear function. If the relationship is dependent, you will need to use a different type of function, such as a quadratic or exponential function.

Q: Can I use the function $y = 2x - 6$ to model a relationship between two variables that have different distributions?

A: No, the function $y = 2x - 6$ is a linear function and can only be used to model relationships between variables that have the same distribution. If the variables have different distributions, you will need to use a different type of function, such as a distribution function or a probability density function.

Q: How do I determine if a relationship between two variables has the same distribution?

A: To determine if a relationship between two variables has the same distribution, you need to consider the nature of the distribution. If the distribution is the same, you can use a linear function. If the distribution is different, you will need to use a different type of function, such as a distribution function or a probability density function.

Q: Can I use the function $y = 2x - 6$ to model a relationship between two variables that are not normally distributed?

A: No, the function $y = 2x - 6$ is a linear function and can only be used to model relationships between variables that are normally distributed. If the variables are not normally distributed, you will need to use a different type of function, such as a non-linear function or a distribution function.

Q: How do I determine if a relationship between two variables is normally distributed?

A: To determine if a relationship between two variables is normally distributed, you need to consider the nature of the distribution. If the distribution is normal, you can use a linear function. If the distribution is not normal, you will need to use a different type of function, such as a non-linear function or a distribution function.

Q: Can I use the function $y = 2x - 6$ to model a relationship between two variables that have different levels of measurement?

A: No, the function $y = 2x - 6$ is a linear function and can only be used to model relationships between variables that have the same level of measurement. If the variables have different levels of measurement, you will need to use a different type of function, such as a scaling function or a normalization function.

Q: How do I determine if a relationship between two variables has the same level of measurement?

A: To determine if a relationship between two variables has the same level of measurement, you need to consider the nature of the measurement. If the measurement is the same, you can use a linear function. If the measurement is different, you will need to use a different type of function, such as a scaling function or a normalization function.

Q: Can I use the function $y = 2x - 6$ to model a relationship between two variables that are not correlated?

A: No, the function $y = 2x -