1. Proportional and Non-Proportional Relationships
Lesson 4.4

2. Proportional vs Nonproportinoal
What does linear mean?
It forms a line.
When you evaluate a table, how do you know if it is proportional or non-proportional?
See if there is a constant slope.
Formula: 𝑦 𝑥 or 𝑦 𝑦 1
𝑥 𝑥 1
If there is a constant, the table is proportional.
When you evaluate a graph, how do you know if it is proportional or non-proportional?
Does the line go through the origin….if it does it is proportional. If the line does not go through the origin, it is not proportional.

3. Example #1:
Look at Example #1 on page Please draw out the graph on your notes.
Is the graph proportional or nonproportional and explain your reasoning in a complete sentence.
How could you find the slope and y-intercept of this graph?
First step: plot points on the line.
Second step: Find the slope y₂ - y ₁
x₂ - x ₁
Third step: find the y-intercept
If x is zero what is the y-coordinate. That will be your y-intercept.
Forth step: What is the equation of the line y=mx+b

4. Complete “Your Turn” #1 and #2 on page 113 for practice.
Identify if the graph represents a proportional or nonproportional relationship and explain why…
Find the slope and y-intercept of each line.
Write an equation for each graph.
Answer #1:
The graph is nonproportional because the line does not go through the origin.
Slope: Y-Intercept: 1
Equation: y=1x+1
Answer #2:
The graph is proportional because the line goes through the origin.
Slope: ¼ Y-Intercept: 0
Equation: y=1/4x+0 or y=1/4x

5. Mexican Pesos Received
Example#3:
The values in the table represent the numbers of U.S. dollars three tourists traded for Mexican pesos. The relationship is linear. Is the relationship proportional or non-proportional
Find the slope using ordered pairs.
Are the slopes in the table constant?
Is this table proportional or non-proportional (Please explain your reasoning).
U.S. Dollars Traded
(X Value)
Mexican Pesos Received
(Y Value)
130
1,690
255
3,315
505
6,565

6. Directions for “Your Turn”
Please complete “Your Turn” #9 and 10 on page 115.
Please give an explanation on why the table is proportional or non-proportional.

7. Example #4: Read Example #4 on page 116. Read Part B to example #4
What is the slope for Arena A?
What is the y-intercept for Arena A?
What is the slope for Arena B?
What is the y-intercept for Arena B?
Read Part B to example #4
What is the slope for Painter A?
What is the y-intercept for Painter A?
What is the slope for Painter B?
What is the y-intercept for Painter B?
Complete “Your Turn” on page 117 #11.