The table below gives the quantity of a product demanded and the quantity supplied for various prices. Solve the
problem.
-Find the linear equation that gives the price as a function of the quantity demanded. $\begin{array}{l|l|l}
\text { Price (dollars) } & \text { Quantity Demanded } & \text { Quantity Supplied } \
\hline 100 & 850 & 0 \
120 & 830 & 30 \
140 & 810 & 60 \
160 & 790 & 90 \
180 & 770 & 120
\end{array}$

A) $p = - q + 950$
B) $p = q + 950$
C) $\mathrm { p } = \frac { 2 } { 3 } \mathrm { q } + 100$
D) $p = - \frac { 2 } { 3 } q + 100$

Question

The table below gives the quantity of a product demanded and the quantity supplied for various prices. Solve the
problem.
-Find the linear equation that gives the price as a function of the quantity demanded. $\begin{array}{l|l|l}
\text { Price (dollars) } & \text { Quantity Demanded } & \text { Quantity Supplied } \
\hline 100 & 850 & 0 \
120 & 830 & 30 \
140 & 810 & 60 \
160 & 790 & 90 \
180 & 770 & 120
\end{array}$

A) $p = - q + 950$
B) $p = q + 950$
C) $\mathrm { p } = \frac { 2 } { 3 } \mathrm { q } + 100$
D) $p = - \frac { 2 } { 3 } q + 100$

Quizplus · Accepted Answer

To find the linear equation that gives the price as a function of the quantity demanded, we can use two points from the table and find the slope ($m$) of the line. Using the points (850, 100) and (830, 120), the slope $m = (120 - 100) / (830 - 850) = 20 / (-20) = -1$. The equation of the line in slope-intercept form is $p = mq + b$. Substituting one point into the equation to solve for $b$, using point (850, 100): $100 = -1(850) + b$, solving for $b$ gives $b = 950$. Thus, the equation is $p = -q + 950$.

The Table Below Gives the Quantity of a Product Demanded