Question 150623
Find the demand equation (p = mx+b) if p = $20 when x = 42 and p = $10 when x = 52.
First, you can find the slope, m, of the line represented by this equation.
p is the dependent variable and x is the independent variable.
{{{m = (p[2]-p[1])/(x[2]-x[1])}}} Make the substitutions: {{{p[1] = 20}}}, {{{p[2] = 10}}}, {{{x[1] = 42}}}, and {{{x[2] = 52}}}
{{{m = (10-20)/(52-42)}}}
{{{m = (-10)/10}}}
{{{m = -1}}}, so now you can write:
{{{p = (-1)x+b}}} but now you need to find b, the p-intercept. Just substitute the p- and x-values from the given data, but make sure that you match the appropriate p with the right x (in other words, mind your p's and x's...lol).
Let's use {{{p[1] = 20}}} and {{{x[1] = 42}}}
{{{20 = (-1)(42)+b}}} Simplify.
{{{20 = -42+b}}} Add 42 to both sides.
{{{62 = b}}}
Now you can write your final equation:
{{{p = -x+62}}}
Check:
{{{p = -x+62}}} Substitute x = 42.
{{{p = -42+62}}}
{{{p = 20}}} OK
{{{p = -x+62}}} Substitute x = 52.
{{{p = -52+62}}}
{{{p = 10}}} OK
Here's the graph of the demand equation: (The vertical axis is p and the horizontal axis is x)
{{{graph(400,400,-5,65,-5,65,-x+62)}}}