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#13
Check
Skills Review
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REASONING The table shows the weights (in pounds) and the prescribed dosages (in milligrams) of medicine for six patients.

Weight
(lb),x
Dosage
(mg),y

94
72

119
90

135
103

150
115

185
140

202
156

a. Find an equation of the line of best fit. Round the slope and the
y-intercept to the nearest tenth, if necessary.

\# $13$ $\newline$ Check $\newline$ Skills Review $\newline$ Listen $\newline$ REASONING The table shows the weights (in pounds) and the prescribed dosages (in milligrams) of medicine for six patients. $\newline$ \begin{tabular}{|l|l|} $\newline$ \hline Weight $(\mathrm{lb}), x$ & Dosage $(\mathrm{mg}), y$ \\ $\newline$ \hline $94$ & $72$ \\ $\newline$ \hline $119$ & $90$ \\ $\newline$ \hline $135$ & $103$ \\ $\newline$ \hline $150$ & $115$ \\ $\newline$ $185$ & $140$ \\ $\newline$ \hline $202$ & $156$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ a. Find an equation of the line of best fit. Round the slope and the $y$ -intercept to the nearest tenth, if necessary.

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Add, subtract, multiply, and divide fractions and mixed numbers: word problems

Full solution

Q. \#

13

\newline

Check

\newline

Skills Review

\newline

Listen

\newline

REASONING The table shows the weights (in pounds) and the prescribed dosages (in milligrams) of medicine for six patients.

\newline

\begin{tabular}{|l|l|}

\newline

\hline Weight

(\mathrm{lb}), x

& Dosage

(\mathrm{mg}), y

\\

\newline

\hline

94

&

72

\\

\newline

\hline

119

&

90

\\

\newline

\hline

135

&

103

\\

\newline

\hline

150

&

115

\\

\newline

185

&

140

\\

\newline

\hline

202

&

156

\\

\newline

\hline

\newline

\end{tabular}

\newline

a. Find an equation of the line of best fit. Round the slope and the

y

-intercept to the nearest tenth, if necessary.

Calculate Slope: First, let's calculate the slope $m$ of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ . We can pick two points from the table, let's use $(94, 72)$ and $(202, 156)$ .
Find Y-Intercept: Now, $m = \frac{156 - 72}{202 - 94} = \frac{84}{108} = 0.77777777778$ , which we round to $0.8$ to keep it to the nearest tenth.
Use Point-Slope Formula: Next, we need to find the $y$ -intercept ( $b$ ) of the line. We can use the point-slope formula $y - y_1 = m(x - x_1)$ with one of the points and the slope we just found. Let's use the point $(94, 72)$ again.
Solve for Y-Intercept: So, $72 - b = 0.8(94 - x)$ . To find $b$ , we need to solve for $b$ when $x$ is $0$ . So, $72 - b = 0.8(94)$ .
Write Equation of Line: Calculating that gives us $72 - b = 75.2$ . Now, we solve for $b$ by adding $b$ to both sides and subtracting $72$ from both sides, which gives us $b = 75.2 - 72$ .
Write Equation of Line: Calculating that gives us $72 - b = 75.2$ . Now, we solve for $b$ by adding $b$ to both sides and subtracting $72$ from both sides, which gives us $b = 75.2 - 72$ . So, $b = 3.2$ . Now we have both the slope and the y-intercept, so we can write the equation of the line of best fit.
Write Equation of Line: Calculating that gives us $72 - b = 75.2$ . Now, we solve for $b$ by adding $b$ to both sides and subtracting $72$ from both sides, which gives us $b = 75.2 - 72$ . So, $b = 3.2$ . Now we have both the slope and the y-intercept, so we can write the equation of the line of best fit. The equation of the line is $y = 0.8x + 3.2$ . This is the line of best fit for the data provided.

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