Graphs & linear equations assign
- 1. Lial: 9.4, 9.5 1
- 2. Graphing Points We have graphed points on a line such as this. a = 3½ 3½ 1 2 3 4 5 But the truth is we do not live in a strictly linear world. We live in a 3 dimensional world and write in a 2 dimensions. So how can we graph a point somewhere above or below the line? Lial: 9.4, 9.5 2
- 3. The Coordinate Grid This is the reason why we have and use the coordinate grid. We not only have the horizontal axis but now add a vertical axis. Because we now have a y vertical and a horizontal line we will label them for easy identification. The horizontal line will be x & the vertical line will be y. (0,0) x The center of the grid is the origin and will always be (0,0), where the x & y are 0. Lial: 9.4, 9.5 3
- 4. The Coordinate Grid From the center where both x & y are zero the numbers will sequentially increase to the right and above and decrease to the left and below. The horizontal axis will have positive numbers on the right and negative numbers on the left. The vertical axis will have positive numbers above the horizontal and negative numbers below. Points to plot on the grid will be given in a parenthesis. Because alphabetically x comes before y, the points are given as (x,y). Lial: 9.4, 9.5 4
- 5. The Coordinate Grid The grid is divided into 4 distinct parts and they have names. Quadrant II Quadrant I (-,+) (+,+) Starting from the upper right and moving counter clockwise we have Quadrant I, II, III, & IV. Quadrant III Quadrant IV Points in Q I will be (+,+), (-,-) (+,-) Q II (-,+), QIII (-,-), & Q IV (+,-). Lial: 9.4, 9.5 5
- 6. Plotting Points on the Coordinate Grid When plotting points always (4,-2) start at the origin. Move left or right first as the x value indicates. At the first (3,5) move you will just hold the spot. c (5,3) From there move up or down as the y value indicates. (4,-2) Once you have moved using both numbers you will note the point with a dot and a label. The point (3,5) will not be the same as (5,3). Lial: 9.4, 9.5 6
- 7. Plotting Points on the Coordinate Grid Plot the following points: (2,3), (-4,6), (-4,6) (0,-5), (-1,-2) (2,3) (-1,-2) (0,-5) Lial: 9.4, 9.5 7
- 8. Graphing Linear Equations Using the knowledge of graphing x y points we can further use the -2 Put each value in the coordinate grid to graph linear original equation and equations. -1 0 solve for the y. This will They are named linear because if we do 1 go in the chart next to all our work correct the points on the 2 the corresponding graph will form a straight line. value. In linear equations there will usually be both an x & y. -2 + y = 6 -1 + y = 6 Using this example: +2 +2 +1 +1 x+y=6 y=8 y=7 We can find points that will lie on this line. We will begin with a chart. 1+y=6 0+y=6 For the x-coordinates we will always use y=6 -1 -1 -2,-1,0,1,2. Fill these numbers in the y=5 chart. 2+y=6 -2 -2 y=4 Lial: 9.4, 9.5 8
- 9. Graphing Linear Equations x+y=6 x y (-2,8) (-1,7) (0,6) (1,5) -2 8 (2,4) -1 7 0 6 1 5 2 4 --The line looks slightly off because I was unable to place the dots exactly in place. Lial: 9.4, 9.5 9
- 10. Graphing Linear Equations When the linear equation is given in slope intercept form you will choose the x points in a way that will make calculations easier. For example: y = ⅓x + 4 If we pick x = -2,-1,0,1,& 2, our answers for y will be fractions. y = ⅓(-2) + 4 y = -2/3 + 4 y = -2/3 + 12/3 y = 10/3 This can be hard to calculate as well as graph. Instead lets look at what would happen to the denominator if I used -3. y = ⅓ (-3) + 4 y = -1 + 4 y=3 Why did this work out better? The -3 would divide evenly into the denominator of one third. Besides three and negative three what would be a good choice? Lial: 9.4, 9.5 10
- 11. Slope The slope of a line has to do with the direction of the line when x is positive. Consider the red line. Is the line increasing or decreasing as you move to the right? Since it is decreasing the line has a negative slope. Consider the blue line. Is the line increasing or decreasing as you move to the right? Since it is increasing the line has a positive slope. Lial: 9.4, 9.5 11
- 12. Khan Academy and Graphing <a style="color: #111; font-family: helvetica;" target="_blank" href="http://www.khanacademy.org/video/algebra-- graphing-lines-1?utm_campaign=embed"> <b>Algebra: graphing lines 1</b>: Graphing linear equations </a><br/> <iframe frameborder="0" scrolling="no" width="560" height="355" src="http://www.khanacademy.org/embed_video?v=2UrcU fBizyw" allowfullscreen webkitallowfullscreen mozallowfullscreen></iframe> 12
- 13. Khan Academy and Graphing http://www.khanacademy.org/math/algebra/linear- equations-and-inequalitie/v/algebra--graphing-lines-1 13