1.3+Finding+Equation+Models

Sept.1.08

SK

UNIT BIG IDEA: Many real world situations can be modeled and predicted using mathematics.
 * Big Idea:**

INV 1 Essential Question: What relationships make a straight line on a graph?
 * Essential Question:**

Notes from Class: None taken


 * Bridge Thickness Experiment (linear)**
 * Thickness (layers) || Breaking weight ||
 * 0 || 0 ||
 * 1 || 8.7 ||
 * 2 || 17.4 ||
 * 3 || 26.1 ||
 * 4 || 34.8 ||
 * 5 || 43.5 ||
 * 6 || 52.2 ||
 * 7 || 60.9 ||
 * 8 || 69.6 ||
 * 9 || 78.3 ||
 * 10 || 87 ||

Since the y-intercept is 0, the line we now know crosses the origin and the y axis and so the pattern is every time Thickness (layer), increases by 1, the breaking weight increases by 8.7. 8.7 is the slope in the y=8.7x . The slope or gradient is the mathematical term which indicates how steep the line of the graph should be and y intercept is related to the slope because that is where the line crosses the origin and slope, here in this case 8.7 decided the steepness of the line. As the thickness increases by 1 the breaking weight increases 8.7 every time 60 = 8.7x 60/8.7 = 6.89, 8.7/8.7 = 1 6.89~ 6.9 6.9 = 1x
 * A.** **Make a table of (x,y) data for y=8.7x, using the x values 0,1,2,3…..10**
 * Explain how the entries in your table relate to the fact that m=8.7 and b=0**
 * B.** **Explain how the slope and the y – intercept of the graph are related to the equation.**
 * C.** **What do the facts that m=8.7x and b=0 means in term of bridge thickness and breaking weight?**
 * D.** **What does the solution tell you about bridge thickness and weight (breaking)?**

The solution tells me that as the x-value is 6.9 the y- value would be 60. So when there would 60 layers the breaking weight would be 6.89~6.9.


 * __Problem 1.3 Follow Up__**

(3, 25) (4,40) 15 / 1 = 15, m = 15 EQUATION: y = 15x -20 40 – 25 = 15 y = 15x + b 4-3 = 1 40 = 15x + b 40 – 60 = -20
 * 1.** **What do the values of m and b in your equation tell you about the graph and about the relationship between bridge thickness and breaking weight for the paper you used?**

The slope in this linear relationship is 15, which decides how steep the graph should be and b tells that the line does not cross the origin, but -20 on the y axis. So the paper we used for the brigde thickness experiment told us that as Thickness or layers increase by 1 the rate of change or the slope between the breaking weight increases by 15.\

A group in Ms. Hollister’s class finds that the equation model y = 5.5x fits their bridge-thickness data. The group conjectures that if they repeat the experiment with cardboard, the relationship will be modeled by y = 4(5.5x) They are saying that the card board is stronger than paper layers and y = 4(5.5x) = 22x saying that y = 22x and this equation is showing that every time you add 1 layer of cardboard the strength goes up 22 units. Cardboard is definitely stronger than paper because it is heavier and thicker materials were used and more materials is used to make the cardboard. Yes it is because inorder to find y in any linear equation you have to multiply x with is co-efficient and multiplication can be done boy ways doesn’t matter which number comes first of the equaton. Y= 5.5 (4x) = y = 5.5 x 4 = **22x;** Y = 4 (5.5x) = y = 4 x 5.5 = **22x** Yes it, because when you multiply y = 4 (5.5x); y 4 x (5.5x) = 22x. The answer of y is 22x 5.5 x 4 = 22x
 * 2a What is group’s conjecture about the strength of the cardboard?**
 * 2b Is y = 5.5 (4x) equivalent to ye = 4 (5.5x)?**
 * Is y = 22x equivalent to y = 4 (5.5x)?**

Problem set with **copied questions (in bold text)** and complete answers (in normal text), be sure to number your work. Show your work/thinking where you can.