Find a linear model for the following data table. Round the slope to three decimal places. $$\begin{array} { | l | l | l | l | l | }
\hline x & 1 & 2.15 & 3.3 & 4.45 \
\hline y & 7 & 11.68 & 16.36 & 21.04 \
\hline
\end{array}$$
A) $y = 4.07 x + 2.93$
B) $y = 2.93 x + 4.07$
C) $y = 4.07 x + 7$
D) $y = 7 x + 4.07$

Question

Find a linear model for the following data table. Round the slope to three decimal places. $$\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 2.15 & 3.3 & 4.45 \
\hline y & 7 & 11.68 & 16.36 & 21.04 \
\hline
\end{array}$$
A) $y = 4.07 x + 2.93$
B) $y = 2.93 x + 4.07$
C) $y = 4.07 x + 7$
D) $y = 7 x + 4.07$

Quizplus · Accepted Answer

To find the linear model, we need to calculate the slope and the y-intercept. Using the formula for the slope of a line, we get:

$$\text{slope} = \frac{\text{change in y}}{\text{change in x}} = \frac{y_2-y_1}{x_2-x_1}$$
$$\text{slope} = \frac{11.68-7}{2.15-1}\approx 4.073$$

To find the y-intercept, we can use the formula for the equation of a line:

$$y = mx + b$$

where m is the slope and b is the y-intercept. Rearranging this equation, we get:

$$b = y - mx$$

We can use any point on the line to find b. Let's use the first point in the table, (1, 7):

$$b = 7 - 4.073(1) \approx 2.927$$

Putting it all together, we get:

$$y = 4.073x + 2.927$$

Rounding the slope to three decimal places, we get:

$$y = 4.07x + 2.93$$

Find a Linear Model for the Following Data Table x12.153.34.45y711.6816.3621.04\begin{array} { | l | l | l | l | l | } \hline x & 1 & 2.15 & 3.3 & 4.45 \\\hline y & 7 & 11.68 & 16.36 & 21.04 \\\hline\end{array}xy​17​2.1511.68​3.316.36​4.4521.04​​

Find a Linear Model for the Following Data Table $\begin{array} { | l | l | l | l | l | } \hline x & 1 & 2.15 & 3.3 & 4.45 \\\hline y & 7 & 11.68 & 16.36 & 21.04 \\\hline\end{array}$