Question

write
in your own words, define the terms point of intersection and break - even point.
remember
the point where two linear graphs intersect repres the solution to both of the equations that describe the graphs.
practice
sofia is the manager of the local video store. she is in charge of buying the videos for the store to sell. she buys videos from a wholesaler that sells them for $8 each. the wholesaler also charges a fee of $200 for each bulk purchase. sofia then sells the videos for $12 each.

1. write an equation to represent the cost to buy videos from the wholesaler. describe what your variables represent. write a second equation to represent the amount of money the store will earn from selling the videos. describe what your variables represent in this equation.
2. calculate the cost to buy 30 videos from the wholesaler.

Explanation:

Step1: Define cost equation variables

Let $x$ = number of videos, $C$ = total cost.
Cost = fixed fee + (cost per video × number of videos)
$C = 200 + 8x$

Step2: Define revenue equation variables

Let $x$ = number of videos, $R$ = total revenue.
Revenue = price per video × number of videos
$R = 12x$

Step3: Calculate cost for 30 videos

Substitute $x=30$ into cost equation:
$C = 200 + 8(30)$
$C = 200 + 240$
$C = 440$

Step4: Define key terms

Point of intersection: The $(x,y)$ point where two lines cross on a graph, satisfying both line equations.
Break-even point: The point where total cost equals total revenue, meaning no profit or loss.

Answer:

1. Cost Equation: $C = 200 + 8x$, where $C$ is the total cost to buy videos, and $x$ is the number of videos purchased.

Revenue Equation: $R = 12x$, where $R$ is the total revenue from selling videos, and $x$ is the number of videos sold.

1. The cost to buy 30 videos is $\$440$.
2. Point of intersection: The shared point where two linear graphs cross, which is a solution for both equations of the graphs.

Break-even point: The point where a business's total costs equal total revenue, meaning no profit or loss is made.