Question 99375
Assuming a line, which represents the relationship between the cost y and the quantity x passes through the points (2,4) and (8,1), find and interpret the slope. Please show your work.
:
Slope formula: m = {{{(y2-y1)/(x2-x1)}}}
:
x1 = 2, y1 = 4
x2 = 8, y2 = 1
:
m = {{{(1 - 4)/(8-2)}}} = {{{(-3)/6}}} = {{{-1/2}}}
:
Find the equation of the line using point/slope formula: y - y1 = m(x - x1)
y - 4 = {{{-1/2}}}(x - 2) 
:
y - 4 = {{{-1/2}}}x + 1
:
y = {{{-1/2}}}x + 1 + 4
:
y = {{{-1/2}}}x + 5 is an equation of the line 
:
Looks like this:
{{{ graph( 300, 200, -6, 10, -10, 10, -.5x + 5) }}}
:
You can interpret, that since it has a negative slope, the more items (x)
produced, the less the cost (y)