Question

The Flip-Flop-Alot Company makes and sells flip-flops. They have one linear function that represents the cost of producing flip-flops and another linear function that models how much income they get from those flip-flops. Describe the key features that would determine if these linear functions ever intercepted.

Answer 1

The cost of producing will have a certain "fixed" portion of the cost, which translates to an offset of the function.

If the company is profitable, the income should be higher than the cost, so the slope of the cost is lower than the slope of the income. So you have two lines, one that "starts high" due to the fixed cost, but has a moderate slope, and one that starts low and has a higher slope. They will intercept at a break-even point.

Answer 2

We can consider two linear functions:

`y_c` and
`y_i` such that
`y_c` represents the the cost of producing flip-flops and
`y_i` represents the income obtained on selling those flip flops.

Now when we plot the graph of these two linear functions then they will meet x and y-axis at some point so the point where the two linear functions intersect will be a break-even point and the point on the x-axis i.e. where y=0 is x-intercept; it represents that there is no income on either selling or purchasing the flip flop

the point where the line touches y-axis i.e. where x=0 is called y-intercept i.e. the cost of either purchasing or selling when no item is sold or purchased.