Thank you for visiting A construction manager is monitoring the progress of building a new house The scatterplot and table show the number of months since the start of. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
We want to find a linear function of the form
[tex]$$
y = m x + b,
$$[/tex]
where [tex]$m$[/tex] is the slope and [tex]$b$[/tex] is the [tex]$y$[/tex]-intercept. The data given is:
[tex]\[
\begin{array}{c|c}
x & y \\
\hline
0 & 100 \\
1 & 86 \\
2 & 65 \\
3 & 59 \\
4 & 41 \\
5 & 34 \\
\end{array}
\][/tex]
Step 1. Compute the slope [tex]$m$[/tex].
The formula for the slope is
[tex]$$
m = \frac{\sum (x - \bar{x})(y - \bar{y})}{\sum (x - \bar{x})^2},
$$[/tex]
where [tex]$\bar{x}$[/tex] and [tex]$\bar{y}$[/tex] are the averages of the [tex]$x$[/tex] and [tex]$y$[/tex] values respectively.
After performing the calculations, the slope is found to be approximately
[tex]$$
m \approx -13.46.
$$[/tex]
Step 2. Compute the [tex]$y$[/tex]-intercept [tex]$b$[/tex].
Once the slope is determined, the [tex]$y$[/tex]-intercept can be calculated using the formula
[tex]$$
b = \bar{y} - m\bar{x}.
$$[/tex]
With the computed values, the intercept is approximately
[tex]$$
b \approx 97.81.
$$[/tex]
Step 3. Formulate the linear equation.
Substituting the values of [tex]$m$[/tex] and [tex]$b$[/tex] into the linear equation gives
[tex]$$
y \approx -13.46\,x + 97.81.
$$[/tex]
Rounding the slope to [tex]$-13.5$[/tex] and the intercept to [tex]$97.8$[/tex], the equation becomes
[tex]$$
y = -13.5\,x + 97.8.
$$[/tex]
Step 4. Identify the correct model.
Comparing with the answer choices:
[tex]\[
\begin{aligned}
\textbf{A: } & y=-13.5 x+97.8 \\
\textbf{B: } & y=-13.5 x+7.3 \\
\textbf{C: } & y=97.8 x-13.5 \\
\textbf{D: } & y=7.3 x-97.8
\end{aligned}
\][/tex]
we see that the equation we obtained, [tex]$y=-13.5 x+97.8$[/tex], corresponds to option A.
Final Answer: Option A.
[tex]$$
y = m x + b,
$$[/tex]
where [tex]$m$[/tex] is the slope and [tex]$b$[/tex] is the [tex]$y$[/tex]-intercept. The data given is:
[tex]\[
\begin{array}{c|c}
x & y \\
\hline
0 & 100 \\
1 & 86 \\
2 & 65 \\
3 & 59 \\
4 & 41 \\
5 & 34 \\
\end{array}
\][/tex]
Step 1. Compute the slope [tex]$m$[/tex].
The formula for the slope is
[tex]$$
m = \frac{\sum (x - \bar{x})(y - \bar{y})}{\sum (x - \bar{x})^2},
$$[/tex]
where [tex]$\bar{x}$[/tex] and [tex]$\bar{y}$[/tex] are the averages of the [tex]$x$[/tex] and [tex]$y$[/tex] values respectively.
After performing the calculations, the slope is found to be approximately
[tex]$$
m \approx -13.46.
$$[/tex]
Step 2. Compute the [tex]$y$[/tex]-intercept [tex]$b$[/tex].
Once the slope is determined, the [tex]$y$[/tex]-intercept can be calculated using the formula
[tex]$$
b = \bar{y} - m\bar{x}.
$$[/tex]
With the computed values, the intercept is approximately
[tex]$$
b \approx 97.81.
$$[/tex]
Step 3. Formulate the linear equation.
Substituting the values of [tex]$m$[/tex] and [tex]$b$[/tex] into the linear equation gives
[tex]$$
y \approx -13.46\,x + 97.81.
$$[/tex]
Rounding the slope to [tex]$-13.5$[/tex] and the intercept to [tex]$97.8$[/tex], the equation becomes
[tex]$$
y = -13.5\,x + 97.8.
$$[/tex]
Step 4. Identify the correct model.
Comparing with the answer choices:
[tex]\[
\begin{aligned}
\textbf{A: } & y=-13.5 x+97.8 \\
\textbf{B: } & y=-13.5 x+7.3 \\
\textbf{C: } & y=97.8 x-13.5 \\
\textbf{D: } & y=7.3 x-97.8
\end{aligned}
\][/tex]
we see that the equation we obtained, [tex]$y=-13.5 x+97.8$[/tex], corresponds to option A.
Final Answer: Option A.
Thank you for reading the article A construction manager is monitoring the progress of building a new house The scatterplot and table show the number of months since the start of. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
