Answer to Question #169766 in Algebra for Ummehani

Question

Two points (p,q) on a linear supply equation are (3.5,116000) and (5,180000)

Determine supply function.

Answer 1

compose the equation of a line at two points:

$\frac{{p - 3.5}}{{5 - 3.5}} = \frac{{q - 116000}}{{180000 - 116000}} \Rightarrow \frac{{p - 3.5}}{{1.5}} = \frac{{q - 116000}}{{{\rm{64000}}}} \Rightarrow q - 116000 = \frac{{{\rm{64000}}}}{{1.5}}\left( {p - 3.5} \right) \Rightarrow$

$\Rightarrow q = \frac{{128000}}{3}p - \frac{{100000}}{3} \Rightarrow q = \frac{{128000p - 100000}}{3}$

Answer: $q = \frac{{128000p - 100000}}{3}$