Question

An economist believes there is a linear relationship between the market price of a particular commodity and the number of units suppliers of the commodity are willing to bring to the marketplace. Two sample observations indicate that when the price equals $15 per unit, the weekly supply equals 30,000 units; and when the price equals $20 per unit, the weekly supply equals 48,000 units.(i) If price per unit, p, is plotted on the horizontal axis and the quantity supplied q is plotted on the vertical axis, determine the slope-intercept form of the equation of the line which passes through these two points. (ii) Interpret the slope of the equation in this application. (iii) Predict the weekly supply if the market price equals $25 per unit​

Answer 1

Step-by-step explanation:

If price p is plotted on the horizontal axis and the quantity supplied q is on vertical axis then the graph will be a line passing through the points with coordinates (15;30000) and (20;48000).

ii)The equation of the line has the form: y=kx+by=kx+b were k=tan\alpha.k=tanα.

Find kk and bb from the system of equations

\begin{cases} 30000=15k+b\\ 48000=20k+b \end{cases};{

30000=15k+b

48000=20k+b

;

\begin{cases} 48000=20k+b \\ 30000=15k+b \end{cases} -;{

48000=20k+b

30000=15k+b

−;

18000=5k;18000=5k;

k=3600;k=3600; tan\alpha=3600;tanα=3600;

30000=15\sdot3600+b \implies b=-24000;30000=15⋅3600+b⟹b=−24000;

q=3600p-24000 -q=3600p−24000− equation of this graph;

iii)If p=35p=35 $ then q=3600\sdot35-24000=102000q=3600⋅35−24000=102000 units;

Answer:If p=35 $ then 102000 units