Question

write
in your own words, define the terms point of intersection and break - even point.
remember
the point where two linear graphs intersect represents 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 to buy videos.
Cost equation: $C = 8x + 200$

Step2: Define revenue equation variables

Let $x$ = number of videos, $R$ = total revenue from selling videos.
Revenue equation: $R = 12x$

Step3: Calculate cost for 30 videos

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

Step4: Define point of intersection

A point where two lines cross, satisfying both equations.

Step5: Define break-even point

The point where total cost equals total revenue, meaning no profit or loss.

Answer:

Definitions:

• Point of intersection: The single point that lies on two different linear graphs, meaning its coordinates satisfy the equations of both lines.
• Break-even point: The point where a business's total costs equal its total revenue; at this point, the business makes no profit and incurs no loss.

Practice 1:

• Cost equation: Let $x$ = number of videos purchased, $C$ = total cost (in dollars) to buy the videos.

$C = 8x + 200$

• Revenue equation: Let $x$ = number of videos sold, $R$ = total revenue (in dollars) from selling the videos.

$R = 12x$

Practice 2:

The total cost to buy 30 videos is $\$440$