6.1+Revisiting+Slopes+0910

AS November 19 Advanced Math 8F

** Big Idea :** The dimensions of a right triangle can be determined with limited information.
 * Essential Question: ** What is “irrational” about Irrational Numbers?
 * Notes: ** Linear equations are Y= MX+B. To find the slope of a line on a graph, you do Y2-Y1 and X2-X1 with two points on the grid and then divide the Y answer by the X answer.


 * __ 6.1 Revisiting Slopes  __**

**The diagram below shows part of the forest. Some of the laser trees have been labeled with letters, and x and y axes have been added. Oskars location is labeled with an O.**

If Oskar had enough power, he could use a laser shield to walk right through the trees. Give the slope of the straight-line path he could follow to get from point O to each of the labeled trees.


 * O to A **
 * Y2-Y1/ X2-X1=S **
 * 0-0/ 7-0=S **
 * 0/ 7=0 **
 * S=0 **
 * O to B **
 * Y2-Y1/ X2-X1=S **
 * 1-0/ 7-0=S **
 * 1/ 7= .143 **
 * S= .143 **
 * O to C **
 * Y2-Y1/ X2-X1=S **
 * 2-0/ 7-0=S **
 * 2/ 7= .286 **
 * S= .286 **
 * O to D **
 * Y2-Y1/ X2-X1=S **
 * 3-0/ 7-0=S **
 * 3/ 7= .429 **
 * S= .429 **


 * O to E **
 * Y2-Y1/ X2-X1=S **
 * 4-0/ 7-0=S **
 * 4/ 7= .571 **
 * S= .571 **
 * O to F **
 * Y2-Y1/ X2-X1=S **
 * 5-0/ 6-0=S **
 * 5/ 6= .833 **
 * S= .833 **
 * O to G **
 * Y2-Y1/ X2-X1=S **
 * 6-0/ 5-0=S **
 * 6/ 5=1.2 **
 * S=1.2 **
 * O to H **
 * Y2-Y1/ X2-X1=S **
 * 7-0/ 4-0=S **
 * 7/ 4=1.75 **
 * S=1.75 **
 * O to I **
 * Y2-Y1/ X2-X1=S **
 * 7-0/ 3-0=S **
 * 7/ 3=2.333 **
 * S=2.333 **
 * O to J **
 * Y2-Y1/ X2-X1=S **
 * 7-0/ 2-0=S **
 * 7/ 2=3.5 **
 * S=3.5 **
 * O to K **
 * Y2-Y1/ X2-X1=S **
 * 7-0/ 1-0=S **
 * 7/ 1=7 **
 * S=7 **

__ Follow Up  __ (4, 14) and (6, 21) are two coordinates that land on the line of OC.
 * 1a. Give the coordinates of two or more trees on OC. **

(10, 12) and (15, 18) are two coordinates that land on the line of OF.
 * 1b. Give the coordinates of two or more trees on OF. **

(1,1), (2,2) and (3,3) are three coordinates that that land on the slope of 1.
 * 2a. Give the coordinates of three trees on the line with slope 1that passes through point O. **

The angle is a 45 degree acute angle.
 * 2b. What angle does the line described in part a make with the x-axis? **

The formula to find its slope is Y2-Y1/X2-X1. You calculate the differences first and then divide Y’s answer by X’s answer.
 * 3. If a line contains two points on a grid, how can you find its slope? **

If a line contained two points on a grid, it would be a rational slope because an irrational slope will never touch a point.
 * 4. If a line contains two points on the grid, will its slope be a rational number or a irrational number? **