The Table Shows Ordered Pairs Of The Function $y = 16 + 0.5x$.$\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline -4 & 14 \\ \hline -2 & 15 \\ \hline 0 & 16 \\ \hline 1 & 16.5 \\ \hline $x$ & $y$ \\ \hline 10 & 21

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Understanding the Function and Ordered Pairs

The given function is $y = 16 + 0.5x$, where $x$ is the input and $y$ is the output. The table shows ordered pairs of this function, which are points on the graph of the function. Each ordered pair consists of a value of $x$ and the corresponding value of $y$. The table provides a visual representation of the function and helps us understand its behavior.

Analyzing the Ordered Pairs

Let's analyze the ordered pairs in the table:

$x$	$y$
-4	14
-2	15
0	16
1	16.5
10	21

From the table, we can see that as $x$ increases, $y$ also increases. This is because the function is linear, and the slope of the line is 0.5, which means that for every unit increase in $x$, $y$ increases by 0.5 units.

Finding the Slope of the Function

The slope of a linear function is the ratio of the change in $y$ to the change in $x$. In this case, the slope is 0.5, which means that for every unit increase in $x$, $y$ increases by 0.5 units. We can also find the slope using the formula:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

where $m$ is the slope, and $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.

Using the Table to Find the Slope

Let's use the table to find the slope of the function. We can choose any two points on the line, such as $(0, 16)$ and $(1, 16.5)$. Then, we can plug these values into the formula:

$$m = \frac{16.5 - 16}{1 - 0} = \frac{0.5}{1} = 0.5$$

This confirms that the slope of the function is indeed 0.5.

Finding the Equation of the Line

Now that we have the slope, we can find the equation of the line using the point-slope form:

$$y - y_1 = m(x - x_1)$$

where $(x_1, y_1)$ is a point on the line, and $m$ is the slope.

Using the Table to Find the Equation

Let's use the table to find the equation of the line. We can choose any point on the line, such as $(0, 16)$. Then, we can plug these values into the formula:

$$y - 16 = 0.5(x - 0)$$

Simplifying the equation, we get:

$$y = 0.5x + 16$$

This is the equation of the line.

Graphing the Function

Now that we have the equation of the line, we can graph the function. The graph of the function is a straight line with a slope of 0.5 and a y-intercept of 16.

Conclusion

In this article, we analyzed the ordered pairs of the function $y = 16 + 0.5x$ and found the slope and equation of the line. We also graphed the function and concluded that it is a straight line with a slope of 0.5 and a y-intercept of 16.

Discussion

The table shows ordered pairs of the function $y = 16 + 0.5x$. The ordered pairs are points on the graph of the function. The function is linear, and the slope of the line is 0.5. We can use the table to find the slope and equation of the line. The equation of the line is $y = 0.5x + 16$. The graph of the function is a straight line with a slope of 0.5 and a y-intercept of 16.

Key Takeaways

• The table shows ordered pairs of the function $y = 16 + 0.5x$.
• The function is linear, and the slope of the line is 0.5.
• We can use the table to find the slope and equation of the line.
• The equation of the line is $y = 0.5x + 16$.
• The graph of the function is a straight line with a slope of 0.5 and a y-intercept of 16.

Final Thoughts

In this article, we analyzed the ordered pairs of the function $y = 16 + 0.5x$ and found the slope and equation of the line. We also graphed the function and concluded that it is a straight line with a slope of 0.5 and a y-intercept of 16. The table shows ordered pairs of the function, and we can use it to find the slope and equation of the line. The equation of the line is $y = 0.5x + 16$.

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Frequently Asked Questions

In this article, we will answer some frequently asked questions about the table shows ordered pairs of the function $y = 16 + 0.5x$.

Q: What is the function $y = 16 + 0.5x$?

A: The function $y = 16 + 0.5x$ is a linear function that takes an input $x$ and returns an output $y$. The function has a slope of 0.5 and a y-intercept of 16.

Q: What is the slope of the function $y = 16 + 0.5x$?

A: The slope of the function $y = 16 + 0.5x$ is 0.5. This means that for every unit increase in $x$, $y$ increases by 0.5 units.

Q: How do I find the equation of the line?

A: To find the equation of the line, you can use the point-slope form:

$$y - y_1 = m(x - x_1)$$

where $(x_1, y_1)$ is a point on the line, and $m$ is the slope.

Q: Can I use the table to find the equation of the line?

A: Yes, you can use the table to find the equation of the line. Choose any point on the line, such as $(0, 16)$, and plug these values into the formula:

$$y - 16 = 0.5(x - 0)$$

Simplifying the equation, you get:

$$y = 0.5x + 16$$

Q: What is the graph of the function $y = 16 + 0.5x$?

A: The graph of the function $y = 16 + 0.5x$ is a straight line with a slope of 0.5 and a y-intercept of 16.

Q: Can I use the table to find the slope of the function?

A: Yes, you can use the table to find the slope of the function. Choose any two points on the line, such as $(0, 16)$ and $(1, 16.5)$, and plug these values into the formula:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Simplifying the equation, you get:

$$m = \frac{16.5 - 16}{1 - 0} = \frac{0.5}{1} = 0.5$$

Q: What is the equation of the line in the form $y = mx + b$?

A: The equation of the line in the form $y = mx + b$ is:

$$y = 0.5x + 16$$

Q: Can I use the table to find the y-intercept of the function?

A: Yes, you can use the table to find the y-intercept of the function. Choose any point on the line, such as $(0, 16)$, and plug these values into the formula:

$$y = mx + b$$

Simplifying the equation, you get:

$$16 = 0.5(0) + b$$

Solving for $b$, you get:

$$b = 16$$

Q: What is the y-intercept of the function $y = 16 + 0.5x$?

A: The y-intercept of the function $y = 16 + 0.5x$ is 16.

Q: Can I use the table to find the x-intercept of the function?

A: Yes, you can use the table to find the x-intercept of the function. Choose any point on the line, such as $(0, 16)$, and plug these values into the formula:

$$y = mx + b$$

Simplifying the equation, you get:

$$16 = 0.5x + b$$

Solving for $x$, you get:

$$x = \frac{16 - b}{0.5}$$

Q: What is the x-intercept of the function $y = 16 + 0.5x$?

A: The x-intercept of the function $y = 16 + 0.5x$ is not defined, since the function is a straight line and does not intersect the x-axis.

Q: Can I use the table to find the slope of the line in the form $m = \frac{y_2 - y_1}{x_2 - x_1}$?

A: Yes, you can use the table to find the slope of the line in the form $m = \frac{y_2 - y_1}{x_2 - x_1}$. Choose any two points on the line, such as $(0, 16)$ and $(1, 16.5)$, and plug these values into the formula:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Simplifying the equation, you get:

$$m = \frac{16.5 - 16}{1 - 0} = \frac{0.5}{1} = 0.5$$

Q: What is the slope of the line in the form $m = \frac{y_2 - y_1}{x_2 - x_1}$?

A: The slope of the line in the form $m = \frac{y_2 - y_1}{x_2 - x_1}$ is 0.5.

Q: Can I use the table to find the equation of the line in the form $y = mx + b$?

A: Yes, you can use the table to find the equation of the line in the form $y = mx + b$. Choose any point on the line, such as $(0, 16)$, and plug these values into the formula:

$$y = mx + b$$

Simplifying the equation, you get:

$$y = 0.5x + 16$$

Q: What is the equation of the line in the form $y = mx + b$?

A: The equation of the line in the form $y = mx + b$ is:

$$y = 0.5x + 16$$

Q: Can I use the table to find the y-intercept of the line?

A: Yes, you can use the table to find the y-intercept of the line. Choose any point on the line, such as $(0, 16)$, and plug these values into the formula:

$$y = mx + b$$

Simplifying the equation, you get:

$$16 = 0.5(0) + b$$

Solving for $b$, you get:

$$b = 16$$

Q: What is the y-intercept of the line?

A: The y-intercept of the line is 16.

Q: Can I use the table to find the x-intercept of the line?

A: Yes, you can use the table to find the x-intercept of the line. Choose any point on the line, such as $(0, 16)$, and plug these values into the formula:

$$y = mx + b$$

Simplifying the equation, you get:

$$16 = 0.5x + b$$

Solving for $x$, you get:

$$x = \frac{16 - b}{0.5}$$

Q: What is the x-intercept of the line?

A: The x-intercept of the line is not defined, since the function is a straight line and does not intersect the x-axis.

Q: Can I use the table to find the slope of the line in the form $m = \frac{y_2 - y_1}{x_2 - x_1}$?

A: Yes, you can use the table to find the slope of the line in the form $m = \frac{y_2 - y_1}{x_2 - x_1}$. Choose any two points on the line, such as $(0, 16)$ and $(1, 16.5)$, and plug these values into the formula:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Simplifying the equation, you get:

$$m = \frac{16.5 - 16}{1 - 0} = \frac{0.5}{1} = 0.5$$

Q: What is the slope of the line in the form $m = \frac{y_2 - y_1}{x_2 - x_1}$?

A: The slope of the line in the form $m = \frac{y_2 - y_1}{x_2 - x_1}$ is 0.5.

Q: Can I use the table to find the equation of the line in the form $y = mx + b$?

A: Yes, you can use the table to find the equation of the line in the form $y = mx + b$. Choose any point on the line, such as $(0, 16)$, and plug