Question 1033141
i believe they mean that the cost function will generate a straight line.
a linear equation has the maximum exponent of the variable x equal to 1.
y = x is a linear equation.
y = 5 is a linear equation.
y = x + 5 is a linear equation.
y = x^2 + 5 is not because the exponent on the variable is greater than 1.


a linear function will have a constant increase or decrease.


you are given that:
when 20 are produced, the cost was 450.
when 30 were produced, the cost was 650.


the slope intercept form of the equation for a straight line is y = mx + b.
m is the slope.
b is the y-intercept.


the slope is given by (y2-y1) / (x2-x1)


(x1,y1 is one point on the line.
(x2,y2) is another point on the line.


you are given 2 points.


they are (20,450) and (30,650)


if you let (x1,y1) = (20,450) and (x2,y2) = (30,650), then your slope will be (650 - 450) / (30 - 20) which is equal to 200 / 10 which can be simplifies to 20.


your slope is 20 so the equation becomes y = 20x + b


to find b, just replace x and y with the values from one of the points on the line.


using (20,450), the equation becomes 450 = 20*20 + b which becomes 450 = 400 + b.
subtract 400 from both sides of the equation to get 450 - 400 = b which results in b = 50.


your equation is now y = 20x + 50.


when x = 20, the equation tells you that y = 450.
when x = 30, the equation tells you that y = 650.


this agrees with what was given.


when x = 100, the equation tells you that y = 20*100 + 50 which becomes y = 2000 + 50 which becomes y = 2050.


when 100 are produced, the cost will be 2050.


the graph below shows the relationship and the value derived through the formula.


<img src = "http://theo.x10hosting.com/2016/050602.jpg" alt="$$$" </>