1. 4.1 representing linear nonproportional relationships
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2. Let’s Review
Proportional relationships
Two rules: It must ALWAYS pass through the origin (0,0) and be a straight line (Linear)
It has a constant RATE of CHANGE
It has constant of PROPORTIONALITY (k)

3. Review: Write an equation to model the problem
Bowling costs $4 a game and $2.50 for a pair of shoes. Write an equation to represent the given situation. 4x
It cost $25 for a yearly participation fee and $50 a month. Write an equation to represent the given situation.
50x +25
A sales person gets paid $500 a monthly salary and 25% commission on all sales made. Write an equation to represent the given situation.
0.25x +500
A plant starts the experiment at 6cm tall and grows 3cm each day. Write an equation to represent the given situation.
3x + 6

4. Goal:
How can you use tables, graphs and equations to represent linear, non proportional situations?
So what do we need to know?

5. Example 1: Representing linear relationships using tables
The total charge (y) for one person to rent a pair of shoes and bowl (x) games at Baxter Bowling Lanes based on the price shown. Make a table of values for this situation. $2 for a pair of shoes and $3 per game.
Step 1: Make a Table
What is the x variable going to represent in the table?
What is the y value going to represent in the table?
(X) games to bowl 1 2 3 4
(y) Total $

6. Y = 3(1) +2 Y = 3(2) +2 Y = 3(3) +2 Y = 3(4) +2
The equation y = 3x +2 gives the total charge (y) for one person to rent a pair of shoes and bowl (x) games at Baxter Bowling Lanes based on the price shown. Make a table of values for this situation.
Step 2: Fill in the values of the table…model the problem just like the teacher
Y = 3(1) Y = 3(2) Y = 3(3) Y = 3(4) +2
Y = Y = Y = Y =
Y = Y = Y = Y = 14
(X) games to bowl 1 2 3 4
(y) Total $ 5 8 11 14

7. Additional Example #1
The total height, y, of a plant in an experiment that was 5 cm tall at the beginning of the experiment grew 2 cm each day. Write the equation.
Y = 2x + 5
Make a table of the values for this situation Cm 1 2 3 4
Total height 7 9 11 13

8. Definition Linear equation
Is an equation whose solutions are ordered pairs that can form a line on the coordinate plane
Linear equations can be written it the form y = mx + b
Y= answer (y value)
M= slope
X = x value
B (y-intercept)

9. Example 2: Representing Linear relationships using graphs
The diameter of the Douglas fur tree is currently 10 inches when measured at chest height. Over the next 50 years, the diameter is expected to increase at an average grown of 2/5 inch per year. Write an equation.
Y = 2/5 x + 10
Y, the diameter of the tree in inches, after x years. Draw a graph of the equation. Describe the relationship

10. Y = 2/5 x + 10
Step 1: Make a table. Choose several values for x that make sense in context.. Should be could by 1’s, 2’s, 3’s, 5’s, 10’s?
Step 2:Plot the ordered pairs from the table. Then draw a line connect the points to represent possible solutions
Step 3: Is the relationship linear…does the point make a straight line…if YES it is a linear, if not …it is not linear. Is it proportional or nonproportional. Does the line go through the orgin? If yes, it is proportional.
Years 5 10 15 20
Diameter 12 14 16 18

11. Additional Example:
A lake has an average depth of 4 feet. A new dam has just been completed, and the average depth of the lake will increase ¾ foot each day for the next 8 days. Write an equation.
Y = 3/4x + 4
Draw a graph after x days. Describe the relationship?
days 2 4 8
Average depth
5.5 7 10