Graphing lines on the coordinate plane Because you never know when you might have to graph the laser, shot from a very evil alien race, that is sure to destroy your city.

So what is the coordinate plane? The Cartesian coordinate plane was invented by French philosopher Rene Descartes in the 17th century. It was a revolutionary development in math because it allowed algebraic equations to be used to describe geometric shapes, providing the first systematic link between these two fields. x axis Basically a number line Which we use to plot the x part of an ordered pair y axis Basically a number line Which we use to plot the y part of an ordered pair Origin The intersection of the x and y axis on the coordinate plane. It’s coordinates are (0,0) The x axis and y axis also split the coordinate plane into four parts called quadrants (in 5 th grade, you will only have to work with the 1 st quadrant) The first quadrant I This is where we will be working in 5 th grade. In this quadrant all of the x and y values are positive ( +, + ) The second quadrant II In this quadrant all of the x values are negative, but the y values are positive ( -, + ) The third quadrant III In this quadrant all of the x and y values are negative ( -, - ) The fourth quadrant IV In this quadrant all of the x values are positive but the y values are negative ( +, - )

Now how do we plot a point on the coordinate plane? To plot a point on the coordinate plane, we need two values. We need the x value and the y value. This will give us an exact point on the coordinate plane. So, let’s look at this point. To find its x value we start at the origin and see how far over we have to go before we line ourselves up with the point. In this case, we go over a distance of 5. To find its y value we start where we left off at the x value and see how far we have to move up to the point. In this case, we go up a distance of 3. So, this point has an x value of 5 and a y value of 3

Now how do we plot a point on the coordinate plane? So, this point has an x value of 5 and a y value of 3 But everyone knows it’s a pain in the bottom to always say, “That point has an x value of 5 and a y value of 3.” So…. We came up with a format to say the same thing without having to use all of those icky English words….blech …Yes you can tell your language arts teacher that I called them icky English words. The format that we use looks like this: ( x, y ) The x value of a point goes into the x spot and the y value goes into the y spot. So in this case its (5,3)! (5,3)(5,3)

But Mr. Sims, why do you math nerds always make such annoying formats like (x,y) Answer 1: We are too lazy to write really long sentences all the time. Answer 2: It makes it clearer when we are talking with people if we can use symbols Answer 3: If everyone does it the same way, it’s efficient and we can all understand each other Answer 4: Monkeys! Just because monkeys are the answer to everything This format (x,y) is called an ordered pair. So we could say (5,3) is one ordered pair. Using ordered pairs we can describe points very quickly and easily!

What are the ordered pairs for the following points A (4,7) B (8,7) C (9,3) D (8,2) E (4,2) F (1,3) X (5,3)

Brain Break

Now for input – output tables…… What? You may be asking what an input output table has to do with anything. Well it’s one of the places that ordered pairs come from. Take for example the equation y = x + 3 I can make an input – output table for this equation: XProcessY Each of these x and y values can be written as an ordered pair XProcessY Ordered Pair (0,3)(0,3) 1 4 (1,4)(1,4) 2 5 (2,5)(2,5) 3 6 (3,6)(3,6) 6 9 (6,9)(6,9) 8 11 (8,11) We can then plot these points on the graph! Now we can see that our equation is making a line This type of pattern is called an additive pattern because you add something to x to get the y value! Notice it does not go through the origin

But we also have multiplicative patterns A multiplicative pattern is one where you multiply x by something to get y. Take for example the equation y = 2x I can make an input – output table for this equation: XProcessY 0x Each of these x and y values can be written as an ordered pair XProcessY Ordered Pair 0 x 2 0 (0,0)(0,0) 1 2 (1,2)(1,2) 2 4 (2,4)(2,4) 3 6 (3,6)(3,6) 4 8 (4,8)(4,8) 5 10 (5,10) We can then plot these points on the graph! Now we can see that our equation is making a line This type of pattern is called an Multiplicative pattern because you multiply x by something to get the y value! Notice it goes through the origin

Now it’s your turn 1)Grab a partner (not violently) 2)CREATE AN EQUATION (additive or multiplicative…your choice) 3)Make an input – output table for your equation 4)Look at the x and y values on your table and create your ordered pairs 5)Get ready to graph your line on the large classroom coordinate grid