Question 172531
So you need to write the equation: p = mx+b.
Research has found the when p = $20, then x = 42 and when p = $10 then p = 52, so you have two points ((42, 20) and (52, 10)) that can be used to define the curve (line) and can also be used to generate the equation.
First, find the slope of the line using the two given points where x is the independent variable and p is the dependent variable.
{{{m = (p[2]-p[1])/(x[2]-x[1])}}} using the given points (42, 20) and (52, 10), make the appropriate substitutions to get:
{{{m = (10-20)/(52-42)}}}
{{{m = -10/10}}}
{{{m = -1}}}
So you now can write:
{{{p = -x+b}}} To find the value of b, substitute the x- and p-coordinates from either one of the two given points.  Let's use (42, 20)
{{{20 = -42+b}}} Solving for b, we get:
{{{b = 62}}} so now you can write the final equation:
{{{highlight(p = -x+62)}}}