1 00:00:00,766 --> 00:00:06,850 Create a graph of the linear equation 5x plus 2y is equal to 20. 2 00:00:06,850 --> 00:00:14,002 So the line is essentially the set of all coordinate, all x's and y's that satisfy this relationship right over here. 3 00:00:14,002 --> 00:00:17,890 To make things simple what we're going to do is we're going to set up a table where we're going to put a bunch of x values in 4 00:00:17,890 --> 00:00:20,425 and then figure out the corresponding y value based on this relationship. 5 00:00:20,441 --> 00:00:26,587 But to make it a little bit simpler, I'm going to solve for y here so it becomes easier to solve for y for any given x. 6 00:00:26,587 --> 00:00:32,578 So we have 5x plus 2y is equal to 20. 7 00:00:32,578 --> 00:00:36,246 If we want to solve for y, let's just get rid of the 5x on the left hand side, 8 00:00:36,246 --> 00:00:39,915 so let's subtract 5x from both sides of this equation. 9 00:00:39,915 --> 00:00:43,166 The left hand side, these guys cancel out. 10 00:00:43,166 --> 00:00:48,506 So we get 2y is equal to the right hand side, you have 20 minus 5x. 11 00:00:48,506 --> 00:00:52,918 And then you can divide both sides of this equation by 2. 12 00:00:52,918 --> 00:00:54,915 So you divide both sides by 2. 13 00:00:54,915 --> 00:00:59,931 The left hand side we just have a y, and then the right hand side... we kind of leave it that way. 14 00:00:59,931 --> 00:01:06,850 That actually would be a pretty straight-forward way to leave it, but or we could call this 20 divided by 2 is 10 minus 5x over 2 15 00:01:06,850 --> 00:01:10,844 or minus five-halves times x. 16 00:01:10,844 --> 00:01:17,253 Listen, since we're using this let's just come up with a bunch of x values and see what the corresponding y values are and then just plot them. 17 00:01:17,253 --> 00:01:19,575 So let me do this in a new color. 18 00:01:19,575 --> 00:01:21,850 So let me... a slightly different shade of yellow... 19 00:01:21,850 --> 00:01:27,609 So we have x values and let's think about what the corresponding y value is going to be. 20 00:01:27,609 --> 00:01:29,467 So I'll start... well, I can start anywhere. 21 00:01:29,467 --> 00:01:32,764 I'll start at x equals zero just 'cause that tends to keep things pretty simple. 22 00:01:32,764 --> 00:01:43,770 If x is zero then y is equal to 10 minus five-halves times zero which is equal to five-halves times zero is just a zero. 23 00:01:43,770 --> 00:01:46,185 So it's just a 10 minus zero or 10. 24 00:01:46,185 --> 00:01:50,667 So that gives us the coordinate, the point, (0,10). 25 00:01:50,667 --> 00:01:58,259 When x is zero, y is 10. So zero, so x is zero so it's going to be right here in the middle of the x axis. 26 00:01:58,259 --> 00:02:00,163 And then you go up 10 for the y coordinate. 27 00:02:00,163 --> 00:02:06,572 [counting] 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. 28 00:02:06,572 --> 00:02:08,104 So, it's right over here. 29 00:02:08,104 --> 00:02:12,067 So that's the point (0,10). 30 00:02:12,067 --> 00:02:16,231 Let's do another point. Let's say that x is 2. 31 00:02:16,231 --> 00:02:20,597 I'm going to pick multiples of two here, just so that I've got a nice, clean answer, here. 32 00:02:20,597 --> 00:02:28,445 So when x is 2, then y is equal to 10 minus five-halves times 2. 33 00:02:28,445 --> 00:02:33,925 And the 2 in the denominator cancels out with the 2 in the denomin... in the numerator. 34 00:02:33,925 --> 00:02:37,501 So simplifies to 10 minus 5 or just 5. 35 00:02:37,501 --> 00:02:38,848 So that tells us the point. 36 00:02:38,848 --> 00:02:43,910 x equals 2, y is equal to 5 is on the line. 37 00:02:43,910 --> 00:02:49,000 So, 2, x is equal to [counting] one, two, right over here, and y is equal to 5. 38 00:02:49,000 --> 00:02:49,900 We go up five. 39 00:02:49,900 --> 00:02:54,266 [counting] 1, 2, 3, 4, 5. And just like that. 40 00:02:54,266 --> 00:02:55,938 So that's the point (2,5). 41 00:02:55,938 --> 00:02:59,067 Now, when you're drawing a line, you actually just need two points. 42 00:02:59,067 --> 00:03:01,603 Actually, if you have a ruler or any straight edge, we can just connect these two points. 43 00:03:01,603 --> 00:03:08,105 And if we do it neatly, every... every point on that line should satisfy this relationship right here. 44 00:03:08,105 --> 00:03:10,241 Just so we get practice, I'll do more points. 45 00:03:10,241 --> 00:03:14,606 So let me do... let's say I want x is equal to 4. 46 00:03:14,606 --> 00:03:19,576 Then y is equal to 10 minus five-halves times four. 47 00:03:19,576 --> 00:03:24,266 This is equal to five-halves times 4, this is equal to 10, right? 48 00:03:24,266 --> 00:03:27,563 'cause the two... divide the denominator by 2; you get 1. 49 00:03:27,563 --> 00:03:29,667 Divide the numerator by 2, you get 2. 50 00:03:29,667 --> 00:03:33,600 Or four over two is the same thing as 2, so it becomes 2 times 5 is 10. 51 00:03:33,600 --> 00:03:40,566 10 minus 10 is a ZERO, so the point (4,0) is on our line. 52 00:03:40,566 --> 00:03:46,604 So, x is [counting] 1, 2, 3, 4, and then y is zero so we don't move up at all. 53 00:03:46,604 --> 00:03:50,504 So we have four... (4,0). 54 00:03:50,504 --> 00:03:53,430 And I could keep going. I can try other points. 55 00:03:53,430 --> 00:03:56,933 You could do them if you like, but this is plenty. Just two of these would have been enough to draw the line. 56 00:03:56,933 --> 00:04:01,333 So let me just, let me just draw it, so I'll do it in white. 57 00:04:01,333 --> 00:04:04,111 So the line will look something like this. 58 00:04:04,111 --> 00:04:12,842 The line will look something... the line will look something like... something like that. 59 00:04:12,842 --> 00:04:15,267 And I can keep going in both directions. 60 00:04:15,267 --> 00:04:16,667 So there you have it. 61 00:04:16,667 --> 00:04:19,111 That is the graph of our linear equation. 62 00:04:19,111 --> 00:04:24,777 Let me make the line, my line a little bit bolder just in case you found that first line hard to read. 63 00:04:24,777 --> 99:59:59,999 So maybe we can make it a little bit bolder. I think you get the general idea.