Graphs, Relations and Functions Cornell Notes #16

Graphing Linear Equations Example Step 1 Step 2 Find ordered pair (x, y), that when substituted into the equation, makes the equation true. Find three ordered pairs that are solutions to the linear equation. 4x + 2y = -8 Note: substitute x=0, then y=0, and then a number you choose for the third value. Substitute 0 for x. So, 4 (0) + 2y = -8 0 + 2y =-8 then, divide both sides by 2 2y = -8 then, simplify 2 2 y= -4 so 1st coordinate point is (0, -4) Substitute 0 for y. So, 4x + 2(0) = -8

Step 2 continued Step 3 4x + 0 = -8 then, divide both sides by 4 4x = -8 then simplify 4 4 x= -2 So the 2nd coordinate point is (-2, 0) Choose your own number. I chose x=2..So, 4(2) + 2y = -8 Substitute in for x 8+2y=-8 then, subtract 8 from each side 8-8 + 2y= -8 -8 then, simplify 0 +2y = -16 then, divide both sides by 2 2y = -16 simplify 2 2 y = -8 So the 3rd coordinate point is (2, -8)

Graph paper project Overview

Practice: Work problem together 4x + 3y = 12 Make a 4 quadrant worksheet. Draw, label x axis, 1-10 Draw , label y axis 1-10 Label quadrants Label coordinate pair in each quadrant Example: quadrant I (x, y) is (+, +) Work x=0 in quadrant I Work y=0 in quadrant II Work x=___ in quadrant III Write table in quadrant IV

Independent Practice Set up your paper and work out the following linear equation. 4x + 3y =18 X-9y=-72 6x+y=21 2x-5y=0

What makes a pattern linear or nonlinear? Linear and Nonlinear Relations What does linear mean? There is a common difference between terms: 5, 10,15, 20 difference is 5 If the rate of change (y/x) is constant, the relationship is linear. A straight line.

This table represents a function. How do I find if the relationship between x and y is linear? Find the differences between the y’s Move from -4 to -3 on the number line, how far did you move? 1 Between -3 and -1 is 2 Between -1 and 2 is 3 Between 2 and 6 is 4 Now find the differences between the x’s x y -5 -4 -3 1 -1 7 2 15 6

This table represents a function. How do I find if the relationship between x and y is linear? Are the y/x the same for each row? Now find the differences between the x’s Between -5 and -3 is 2 Between -3 and 1 is 4 Between 1 and 7 is 6 Between 7 and 15 is 8 ½, 2/4, 3/6, 4/8 All these fractions reduce to ½ so the relationship is linear. x y -5 -4 -3 1 -1 7 2 15 6

Is the relationship between x and y linear or nonlinear? Independent Practice Is the relationship between x and y linear or nonlinear? x y -2 -9 -5 3 1 4 7 9

Application Jonny just bought a computer that came with 4 games already installed on it. Each week, he downloads 2 more computer games. Write an equation that represents the number of games. Make a table for 5 weeks, and number of games each week. Graph your answer.