4.1 Using Graphs to Relate Two Quantities: Interpret: To establish or explain the meaning or significance of something. Analyze: to examine something in great detail in order to understand it better. Describe: To give an account of something by giving details of its characteristics
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4.1 Using Graphs to Relate Two Quantities: Interpret: To establish or explain the meaning or significance of something. Analyze: to examine something in.
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4.1 Using Graphs to Relate Two Quantities:
Interpret: To establish or explain the meaning or significance of something.
Analyze: to examine something in great detail in order to understand it better.
Describe: To give an account of something by giving details of its characteristics
Graphs:
In math we use graphs to represent real world situations. A well rounded Algebra 1 student must be able to work with graphs and be able to:
1. Analyze graphs,
2. Match graphs to given situations, and
3. Sketch graphs
Analyzing Graphs: Given any graph, we must be able to describe the information it is providing by using the labeling (variables) of each graph.
Ex:
Looking at the labels of the graph(variables), we can see that this graph has to do with volume of a balloon (vertical label: y-axis) over time (horizontal label: x-axis).
This means, that as time goes by, the volume in the balloon increases.
YOU TRY IT:
a) What are the variables in the graph?
Depth
Tem
p (F
o )
b) Describe how the variables are related.
Temperatures of H20
YOU TRY IT: (Solution)
a) The variables are depth (Independent) and temperature (dependent)
DepthTe
mp
(Fo )
b) The temperature of the water decreases as depth increases.
Temperatures of H20
Matching graphs: Data from a table is often displayed using a graph to visually represent the relationship between the variables. It is our job to math the corresponding table with the graph.
Ex:
Matching graphs: looking at the table, from point to point, we see that it increases rapidly from one to the other (not constant) which means it is not going to create a line. The answer is B.
Ex:
YOU TRY IT:
Match the graph to the proper situation.
YOU TRY IT: (SOLUTION)
Match the graph to the proper situation.
4) C: The first point is (1, 50)
5) B: The first point is (1, 80)
6) A: The first point is (1, 60)
Sketching Graphs: Data from a given situation can be transferred to a graph. We must once again keep in mind the Independent variable (x) and the independent variable (y). JESSIE WAS HERE
Ex:
Sketching Graphs (SOLUTION):
YOU TRY IT:
Sketch the graph to represent the following situation.
1) Suppose you want to buy several cans of soup that cost $2.00 each. How is the cost related to the number of cans you buy.
YOU TRY IT: (SOLUTION)We know that each can costs $2.00