5.2+++Finding+the+Slope+of+a+Line+10-11

May 31st 2011 Math 7B Caroline Beninger Big Idea: Many real world situations canbe modeled and predicted using mathematics. Essential Question: How steep is thatline? Problem 5.2 Finding the Slope of a Line: i. y=2x **﻿** ii. y=-3x iii. y=5+2x iv. y=1/2x+2 v. y=2-3x i. X Y -3 -6 -2 -4 -1 -2 0 0 1 2 2 4 3 6 4 8 ii. X Y -3 9 -2 6 -1 3 0 0 1 -3 2 -6 3 -9 4 -12 iii. X Y -3 -1 -2 1 -1 3 0 5 1 7 2 9 3 11 4 13 iv. X Y -3 0.5 -2 1 -1 1.5 0 2 1 2.5 2 3 3 3.5 4 4 v. X Y -3 11 -2 8 -1 5
 * Do parts A-D for each equation below. **
 * A. Make a table of the x and y values for the equation. Use the x values -3,-2, -1, 0, 1, 2, 3, and 4 **

1 -1 2 -4 3 -7 4 -10 i. black ii. red iii.blue iv. green v. orange
 * B. On grid paper make a graph of the equation. **

Yes, if you choose two points on the line for any of the equations and compute the ratio of vertical and horizontal change from one point to another you would get the same ratio as you would have if you had chosen two other points because the lines are constant which means that are always staying the same and repeating their patterns. The ratio I computed in part C, the slope of a line, is related to the values of the line because values are what make slopes. __ Follow Up: __ The line for y=3x is steeper than the line for y=x because it means that Y goes up 3 times for every time for X with the equation y=3x but for the equation y=x it only goes up by one each time.
 * C. If you choose two points on the line, and compute the ratio of vertical change to the horizontal change from one point to the other. Would you get the same ratio if you had chosen two different points? **
 * D. The ratio you computed in part C is the slope of a line, How is the slope of the line related to the table of values for the line? how is it related to the equation for the line? **
 * Follow-Up ****﻿** ** Use the ideas you have learned about slope and about vertical and horizontal **** change to explain why the line of y=3x is steeper than the line for y=x. **