2. Intersecting lines
Finding the point of intersection of two curves is a form of solving simultaneous equations.
One example of simultaneous equations is finding a break even point.
This type of question will often involve one equation for the cost of the goods produced and a second equation for the revenue (or income) from sales of the goods.
The point at which the 2 lines meet is called the break even point.
At this point the costs equal the revenue.
On one side of this point (normally the left), the costs exceed the revenue, so there is a loss of money.
On the other side of this point (normally the right), the revenue exceeds the costs, so a profit is made.

3. Example 1
Sarah was planning a disco. The cost of hiring the 80’s juke box was $135 and food for the guest was $5·50 per head. Sarah charged $10 per person to attend.
Revenue
Form equations for the cost and revenue for the disco.
Plot the lines
What is the break even point?
C = ·5n
R = 10n n 10 20 40 C
135
190
245
355 n 10 20 40 R
100
200
400 c)
30 guests

4. Example 2
Tim makes greeting cards at home to sell at his retirement village. He needed to purchase $90 worth of pens and nibs at the start and each card costs $2·75 in paper and ink to make. Tim sells the cards for $5 each.
Cost
Revenue
Form equations for the cost and revenue of the cards.
Plot the lines
What is the break even point?
C = ·75n
R = 5n n 8 24 40 C 90
112
156
200 n 10 20 30 R 50
100
150 c)
40 cards

5. Today’s work
Exercise 12B pg 364
#2, 4, 6