1.3+Finding+Equation+Models+0910

JO**
 * 23/8/09
 * Big Idea:** Many real world situations can be modeled and prediced using mathematics
 * Essential Question:** What relationships make a straight line on a graph?
 * Notes from Class:

1.3

A. Make a table of (x,y) data and explore the equation y=8.7x** The "M" is the slope which is 8.7 which is how much the y axis goes up by, and the positive number starts at 0 which is "B" which is the y-intercept.
 * X || Y ||
 * 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 ||

**
 * B. Make a graph of y=8.7x for x=0 to x=10. Explain how the slope and the y-intercept of the graph are related to the equation.

The slope in the graph is related to the equation because the graph goes up by 8.7 which is the slope. And the y-intercept of the graph is related to the equation because the y coordinate 0 goes across the y-axis which is the y-intercept.


 * C. What do the facts that m=8.7** **and b=0 mean in terms of bridge thickness and breaking weight?**

m=8.7 means that in their experiment it took on average 8.7 pennies more to break each thickness and b=0 means that if there is no bridge thickness, it will take no pennies to break it


 * D. Solve the equation 60=8.7x. What does the solution tell you about bridge thickness and breaking weight?**

60 = 8.7 x 6.9. This means that if the thickness is 7 layers, at least 60 pennies would break it.


 * F.U

1. Find a linear equation for the graph model from your bridge thickness experiment. What do the values of m and b in your equation tell you aout the graph and about the relationship between bridge thickness and breaking weight for the paper you used?**

Y=10x. This tells me that my slope is 10 and that my y intercept is 0. And this predicts the breaking weight for amount of layers thick since the amount of layers is x and it took me 10 pennies to bend one paper bridge.

A. What is this group's conjecture about the strenght of cardboard?**
 * 2. 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 if they use cardboard, its going to be 4 times stronger


 * B. Is y=5.5(4x) equivalent to y=4(5.5x)? Is y=22x equivalent to y=4(5.5x)? Give evidence to support your answers**

Yes they are equivalent to each other. For the first equivilation set, for multiplication, the order doesn't really matter because it doesn't affect the answer. For example: 2x4=8 and 4x2=8 have the same answer although it was switched around. For the second equivalent set, if you multiply any number by 5.5, then multiplying it by 4, would give you the same answer as mulitplying any number by 22. Because 4 multiplied by 5.5 equals 22. And like I said in the first set, the order of multiplication doesn't matter