The following table shows the depth D , in inches, of water in a pond after $d$ days of eva- poration. Find a linear model for depth as a function of days. $$\begin{array} { | l | l | l | l | l | }
\hline d & 4 & 6 & 8 & 10 \
\hline D & 779 & 777 & 775 & 773 \
\hline
\end{array}$$
A) $D = - 2 d + 787$
B) $D = 783 d + - 1$
C) $D = - 1 d + 783$
D) $D = 787 d + - 2$

Question

The following table shows the depth D , in inches, of water in a pond after $d$ days of eva- poration. Find a linear model for depth as a function of days. $$\begin{array} { | l | l | l | l | l | } 
\hline d & 4 & 6 & 8 & 10 \
\hline D & 779 & 777 & 775 & 773 \
\hline
\end{array}$$
A) $D = - 2 d + 787$
B) $D = 783 d + - 1$
C) $D = - 1 d + 783$
D) $D = 787 d + - 2$

Quizplus · Accepted Answer

To find a linear model, we need to find the slope and y-intercept of the line that passes through the given points. Using the points (4, 779) and (10, 773), we get a slope of $(773-779)/(10-4)=-1$. Using the slope-intercept form $y = mx + b$ and one of the points, say (4, 779), we can solve for the y-intercept $b$: $779 = (-1)(4) + b$, which gives $b = 783$. Putting the slope and y-intercept together, we get $D = -1d + 783$. Therefore, the correct choice is C.

The Following Table Shows the Depth D , in Inches ddd

The Following Table Shows the Depth D , in Inches $d$