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?

DepthTe

mp

(Fo )

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

Cost

$

Cans

Cans(x)

Dollars(y)

1 2

2 4

3 6

4 8

The cost will vary DIRECTLY with # of cans.

VIDEOS: Graphs

https://www.khanacademy.org/math/arithmetic/applying-math-reasoning-topic/reading_data/v/reading-bar-charts-1

https://www.khanacademy.org/math/arithmetic/applying-math-reasoning-topic/reading_data/v/u08-l1-t2-we2-reading-line-graphs

CLASSWORK:

Page 237-239

Problems: As many as needed to master the concept