3.2+Graphing+Lines

5-28-2009 MK // Essential Question #3: How can technology help us explore linear patterns in the world? // __//**3.2 Graphing Lines**//__ i. y=3x ii. y=-2x iii. y=5x-3 iv. y=-x+6 v. y=2 (ii) This means they give you 2$s per mile. (iii) This means you pay 5$s per mile, then, they give you 3$s back. (iv) This means they give you 1$s per mile, then you have to pay 6$s. (v) This means it doesn't matter how many miles you run, you only give 2$s. I think plan 3 is the best one because it makes the most money. Also, even if it isn't, it sounds like a good deal since they give you back 3$s. __//**C.**//__ **Q: Graph each plan in a graphing calculator. Use a window that shows the graph clearly. Make a sketch of the graph you see.** //__D.__// Q:** For each pledge plan, tell whether the y-value increase. decrease, or stay the same as the x-value increase. How can you tell from the graph? From the table? From the equation? Plan ii: The y-value decreases as the x-value icreases. In the table, the x-value increases while the y-value decreases. In the graph, it's shown as a line that goes from the 4th quadrant up to the 2nd quadrant. In the equation, it has a negative coeficient. Plan iii: The y-value increases as the x-value does. In the table, both values increase. In the graph, it's shown as a line that goes from the 3rd quadrant up to the 1st quadrant while passing the 4th quadrant because it has an negative y-intercept. In the equation, it has a positive coeficient with a additional '-3'. Plan iv: The y-value decreases as the x-value icreases. In the table, the x-value increases while the y-value decreases. In the graph, it's shown as a line that goes from the 4th quadrant up to the 2nd quadrant while passing the 1st quadrant because of the positive y-intercept. In the equation, it has a negative coeficient with a additional '+6'. Plan v: The y-value just stays same all the way while the x-value increases. In the table, it shows the same y-value as you go down. In the graph, there is a horizontal line parralel to the x-value that keeps on going forever. In the equation, there's only the y-variable with no x-variable and only the '2'. 1.__// Q:** For each of the five pledge plans, give the coordinates of the points where the line crosses the x and the y-axes. (Check that the coordinates you gave fit the equation. Sometimes the decimal values your calculator gives are only approximations.) Plan ii: x= (0,0) y= (0,0) Plan iii: x= (3/5,0) y= (0,-3) Plan iv: x= (6,0) y= (0,6) Plan v: x= (uhhh... this doesn't have one) y= (0,2) Ali: -3+5(-1)= -3+(5*-1)= -3+-5= -8 Tamara: -3+5(-1)= (-3+5)*-1= 2*-1= -2
 * Big Idea: Many real world situations can be modeled and predicted using mathematics. **
 * __//A.//__** **Q: What does each pledge plan mean?**
 * A:** (i) This means you pay 3$s per mile.
 * __//B.//__** **Q: Without your graphing calculator, make a table with the x-values of 1, 2, 3, 4, and 5. Use these table to decide which plan is reasonable. Explain why.**
 * A:**
 * ~ Table of different plans || Plan 1 || Plan 2 || Plan 3 || Plan 4 || Plan 5 ||
 * 1) of miles ran || y=3x || y=-2x || y=5x-3 || y=-x+6 || y=2 ||
 * 1 || 3$ || -2$ || 2$ || 5$ || 2$ ||
 * 2 || 6$ || -4$ || 7$ || 4$ || 2$ ||
 * 3 || 9$ || -6$ || 12$ || 3$ || 2$ ||
 * 4 || 12$ || -8$ || 17$ || 2$ || 2$ ||
 * 5 || 15$ || -10$ || 22$ || 1$ || 2$ ||
 * 5 || 15$ || -10$ || 22$ || 1$ || 2$ ||
 * A:
 * A:** Plan i: The y-value increases as the x-value does. In the table, both values increase. In the graph, it's shown as a line that goes from the 3rd quadrant up to the 1st quadrant. In the equation, it has a positive coeficient.
 * //__3,2 Follow-Up
 * A:** Plan i: x= (0,0) y= (0,0)
 * //__2.__// Q:** Ali says that x=-1 makes the equation -8=-3+5x true. Tamara tries this value in the equation. She says Ali is wrong because -3+5(-1) is -2, not -8. Why do you think these students found different answers.
 * A:** I think its because they had different problem solving orders.