Have you ever tried to choose between two things that you really wanted to do? Take a look at this dilemma.
The seventh graders have to decide between two field trips. One is bowling and the other is a trip to the Omnitheater. It is time for them to figure out which field trip to attend. Mr. Thomas has scheduled a meeting during homeroom to discuss options.
“I think we should go to the Omni Theater because it is more educational,” Tasha stated strongly.
“This trip doesn’t have to be educational we can just have a fun field trip,” Casey said.
Arguments began between the students. Mr. Thomas whistled and all were quiet.
“Is there anything that the two have in common that we can think of?” Mr. Thomas asked.
“You mean money?” Casey asked.
“Yes. Is there a common fee between them both?”
The students began to think about this. Intercepts are places where two or more equations meet. In the case of the students, they wrote two equations one for each field trip. Is there a common cost in each?
Use this Concept to learn about intercepts and then return to this problem and Mr. Thomas’ question at the end of it.
Guidance
In football, a player makes an interception when he catches a ball thrown by the other team that was not intended for him. Intercept means to catch or to interrupt. In graphs, we will find that most lines intercept the
Consider the graph below. As you know, the
In looking at this graph, you can see that the line crosses the
The line crosses the
The line crosses the
These are the two intercepts.
We can figure out the two intercepts of any linear equation. All you have to do is to look for the place where the line crosses the two axis’.
That is a great question. Because a vertical line is
In these two graphs,
Find the
First, notice that this is an equation in standard form. We will need to find the
To find the
We now have the ordered pair (3, 0) or the
To find the
We now have the ordered pair (0, 2) or the
Consider a graph whose
Look at the following graph and interpret the intercepts of the graph.
Now let’s look at what information we can interpret from this graph. First, this is a graph of the equation
Notice that the coordinates of the
Now we can look at the value of the
Determine the x and yintercepts for each equation.
Example A
Solution: (4,0) and (0,2)
Example B
Solution: (2,0)(0,3)
Example C
Solution: (3,0)(0,4)
Now let's go back to the dilemma from the beginning of the Concept.
To determine the intercept, we must first begin with the two equations.
The bowling trip used the equation
The Omni trip used the equation
You might notice right away that the 2 is common in both. We can check and see if this is indeed the intercept by graphing both equations. Here is the graph.
The $2.00 fee for shoes or ticket service fee is the common factor between both trips.
Vocabulary

x – intercept 
the point where a line crosses the
x – axis. It will always have the coordinates(x,0) .

y – intercept 
the point where a line crosses the
y – axis. It will always have the coordinates(y,0) .
Guided Practice
Here is one for you to try on your own.
Martha likes to go to the park every day but it’s 6 o’clock and her parents are waiting for her at home. She has her bike but she sometimes walks it. She walks at 3mph and she rides her bike at 9mph. If she is 6 miles from home, how long might her parents have to wait?
Solution
If she only rides her bike, it will take her
If she only walks, it will take her 2 hours! Hope she rides her bike.
Video Review
Practice
Directions: Determine the

3x+4y=12 
6x+2y=12 
4x+5y=20 
4x+2y=8 
3x+5y=15 
−2x+3y=−6 
−3x+y=9 
−2x−2y=6 
7x+3y=21 
2x+9y=36
Directions: Look at each graph and identify the