Question 579312
let x equal the cost per cookie box.
let y equal the number of cookie boxes you sell.
you have 2 points that you can use to make a straight line equation.
they are:
(x1,y1) = (3,250)
(x2,y2) = (5,120)
these 2 points can be used to generate a straight line equation using the point slope form.
the point slope form of the equation for a straight line is:
y - y1 = m * (x - x1)
it can also be:
y - y2 = m * (x - x2)
any point that is on the line can be used.
m is the slope of the equation.
the formula to find the slope is:
m = (y2 - y1) / (x2 - x1)
you use both points to find the slope.
substituting for y1 and y2 and x1 and x2, we get:
m = (120 - 250) / (5 - 3)
this becomes:
m = -130 / 2 which becomes:
m = -65
our slope is -65 and our equation becomes:
y - y1 = -65 * (x - x1)
or it becomes:
y - y2 = -65 * (x - x2)
we can use either point.
we'll use (x1,y1) = (3,250)
when we use that point, our equation becomes:
y - 250 = -65 * (x - 3)
we simplify this to get:
y - 250 = -65x + 195
add 250 to both sides of this equation to get:
y = -65x + 195 + 250 which becomes:
y = -65x + 445
that's our equation.
the equation looks like this:
{{{graph(600,600,-10,10,-30,500,-65x+445,250,120)}}}
you can see from the graph that when x = 3, y = 250, and when x = 5, y = 120.
the horizontal lines at y = 250 and y = 120 are there to help you see that.