 This is a video about graphing First the XY coordinate plane. It's made from a horizontal number line called the x-axis and a vertical number line called the y-axis these axes Intersect at a point called the origin So the point of section is called the origin and it's represented by the ordered pair zero zero Now on this coordinate plane we plot ordered pairs Two numbers separated by a comma enclosed within parentheses The first number will be the x-coordinate. The second number will be the y-coordinate On the coordinate plane We have four regions called quadrants quadrant one is in the top right followed by quadrant two three and four in a counterclockwise fashion So let's do some graphing practice I'm going to graph the point three negative seven so my x-coordinates three my y-coordinates negative seven That means on the x-axis we will go right three and Then we will go vertical movement will be down seven three negative seven That is point a That is located in quadrant four Point B seven zero so my horizontal movement seven positive seven and There is no vertical movement. So I have zero point C negative four two That's left four down to and that's going to be in quadrant three Point B is actually directly on the x-axis Now let's find out the ordered pair for each of the points starting with point Q So on the graph we identified point Q of horizontal movements negative two the vertical movements four So negative two or Point R. We have left three so negative three and down three. So also negative three Point S You go right four and up six So four six is the ordered pair for point s Now we're gonna move into graphing linear equations But first we want to figure out what is a linear equation exactly? How do you know if something is a linear equation? Well, that is if the highest power on each variable x and y is one So in part a negative three x plus four y equals two Everything's good x has a power of one y has a power of one. So the answer is yes. It is linear Part B. You have y squared equals x minus five since it's y squared The power of two makes it no not a linear equation Part C to y equals x minus four the highest power on x and y is one in both cases. So the answer there is yes In general we are going to use these solutions to obtain ordered pairs or use these equations to obtain ordered pairs By coming up with solutions x y ordered pairs that satisfy the equation So for instance in the linear equation y equals three times x if X is negative one I can literally plug in negative one for x into the equation to figure out what y is So y equals three times x or three times negative one negative three So my ordered pair is negative one negative three That is going to be a point on the line Or at a point that satisfies this linear equation Y is zero so now y equals three x we let y equals zero so zero equals three x Solve the equation dividing both sides by three And it looks like you get zero equals x Zero zero is the ordered pair Next y is negative nine so I have negative nine equals three x Divide both sides by three and then I'll get negative three equals x So there's another ordered pair linear equations graph lines So if I was to graph these points, they should form a line. You only need two points to form a line, but Three is also a good checks and balances to use so negative one negative three Zero zero and then negative three negative nine notice all three points line up with each other Connect the dots and you've graphed yourself a line Linear equations always form lines when they're graphed Next equation y equals one half x minus five when x is negative two what is y well What's one half times negative two minus five? What is negative one minus five that is negative six so negative two negative six What happens when x is zero y equals one half times zero minus five Zero minus five is negative five X is zero in the ordered pair and y is negative five What happens when y is zero? Well, what is x? So this will be working backwards. We have zero equals one half x minus five Add five to both sides Five equals one half x Multiply everything by two you get ten equals x so ten zero is the ordered pair Let's plot these points Hopefully they do form a line because this is a linear equation starting with negative two negative six zero negative five And ten zero That's a way out here. All right, so those are the three points. They do form a line connect the dots There you have it. There's a line Now we use the equation 3x plus y equals 12 to complete each ordered pair So when x is zero what is y? Well three times zero plus y equals 12 Zero plus y equals 12 guess that means y equals 12 Zero 12 is the ordered pair Part B X is unknown y is six. So we have 3x plus six equals 12 Solve the equation here 3x equals six Divide both sides by three x equals two so two six is the ordered pair Part C Negative one is x what is the coordinate we need for y to satisfy the equation and find the full ordered pair? Well three times negative one plus y equals 12 negative three plus y equals 12 Add three to both sides Why equals 15? So the ordered pair is negative one 15 So that's a little introduction to graphing and how to graph linear equations and complete ordered pairs for Thanks for watching