1 00:00:00,000 --> 00:00:00,640 2 00:00:00,640 --> 00:00:03,430 We're asked to convert these linear equations into 3 00:00:03,430 --> 00:00:08,870 slope-intercept form and then graph them on a single 4 00:00:08,869 --> 00:00:09,739 coordinate plane. 5 00:00:09,740 --> 00:00:11,589 We have our coordinate plane over here. 6 00:00:11,589 --> 00:00:14,719 And just as a bit of a review, slope-intercept form is a form 7 00:00:14,720 --> 00:00:20,910 y is equal to mx plus b, where m is the slope 8 00:00:20,910 --> 00:00:22,510 and b is the intercept. 9 00:00:22,510 --> 00:00:25,050 That's why it's called slope-intercept form. 10 00:00:25,050 --> 00:00:27,019 So we just have to algebraically manipulate these 11 00:00:27,019 --> 00:00:29,439 equations into this form. 12 00:00:29,440 --> 00:00:34,539 So let's start with line A, so start with a line A. 13 00:00:34,539 --> 00:00:39,229 So line A, it's in standard form right now, it's 4x plus 14 00:00:39,229 --> 00:00:42,569 2y is equal to negative 8. 15 00:00:42,570 --> 00:00:46,159 The first thing I'd like to do is get rid of this 4x from the 16 00:00:46,159 --> 00:00:48,879 left-hand side, and the best way to do that is to subtract 17 00:00:48,880 --> 00:00:51,460 4x from both sides of this equation. 18 00:00:51,460 --> 00:00:55,420 So let me subtract 4x from both sides. 19 00:00:55,420 --> 00:00:57,880 The left hand side of the equation, these two 4x's 20 00:00:57,880 --> 00:01:02,440 cancel out, and I'm just left with 2y is equal to. 21 00:01:02,439 --> 00:01:10,479 And on the right-hand side I have negative 4x minus is 8, 22 00:01:10,480 --> 00:01:13,430 or negative 8 minus 4, however you want to do it. 23 00:01:13,430 --> 00:01:15,890 Now we're almost at slope-intercept form. 24 00:01:15,890 --> 00:01:18,329 We just have to get rid of this 2, and the best way to do 25 00:01:18,329 --> 00:01:20,769 that that I can think of is divide both sides of this 26 00:01:20,769 --> 00:01:23,219 equation by 2. 27 00:01:23,219 --> 00:01:25,250 So let's divide both sides by 2. 28 00:01:25,250 --> 00:01:28,189 So we divide the left-hand side by 2 and then divide the 29 00:01:28,189 --> 00:01:29,700 right-hand side by 2. 30 00:01:29,700 --> 00:01:31,750 You have to divide every term by 2. 31 00:01:31,750 --> 00:01:37,980 And then we are left with y is equal to negative 4 divided by 32 00:01:37,980 --> 00:01:40,540 2 is negative 2x. 33 00:01:40,540 --> 00:01:45,070 Negative 8 divided by 2 is negative 4, 34 00:01:45,069 --> 00:01:47,479 negative 2x minus 4. 35 00:01:47,480 --> 00:01:52,900 So this is line A, let me graph it right now. 36 00:01:52,900 --> 00:01:56,420 So line A, its y-intercept is negative 4. 37 00:01:56,420 --> 00:01:59,100 So the point 0, negative 4 on this graph. 38 00:01:59,099 --> 00:02:01,789 If x is equal to 0, y is going to be equal to negative 4, you 39 00:02:01,790 --> 00:02:04,150 can just substitute that in the graph. 40 00:02:04,150 --> 00:02:07,330 So 0, 1, 2, 3, 4. 41 00:02:07,329 --> 00:02:10,978 That's the point 0, negative 4. 42 00:02:10,979 --> 00:02:14,300 That's the y-intercept for line A. 43 00:02:14,300 --> 00:02:18,770 And then the slope is negative 2x. 44 00:02:18,770 --> 00:02:23,830 So that means that if I change x by positive 1 that y goes 45 00:02:23,830 --> 00:02:26,150 down by negative 2. 46 00:02:26,150 --> 00:02:27,460 So let's do that. 47 00:02:27,460 --> 00:02:30,250 So if I go over one in the positive direction, I have to 48 00:02:30,250 --> 00:02:32,870 go down 2, that's what a negative slope's going to do, 49 00:02:32,870 --> 00:02:33,920 negative 2 slope. 50 00:02:33,919 --> 00:02:37,750 If I go over 2, I'm going to have to go down 4. 51 00:02:37,750 --> 00:02:42,460 If I go back negative 1, so if I go in the x direction 52 00:02:42,460 --> 00:02:45,540 negative 1, that means in the y direction I go positive two, 53 00:02:45,539 --> 00:02:48,620 because two divided by negative one is still negative 54 00:02:48,620 --> 00:02:49,849 two, so I go over here. 55 00:02:49,849 --> 00:02:53,389 If I go back 2, I'm going to go up 4. 56 00:02:53,389 --> 00:02:54,299 Let me just do that. 57 00:02:54,300 --> 00:02:56,490 Back 2 and then up 4. 58 00:02:56,490 --> 00:02:59,120 So this line is going to look like this. 59 00:02:59,120 --> 00:03:03,000 60 00:03:03,000 --> 00:03:06,159 Do my best to draw it, that's a decent job. 61 00:03:06,159 --> 00:03:09,549 That is line A right there. 62 00:03:09,550 --> 00:03:13,710 All right, let's do line B. 63 00:03:13,710 --> 00:03:20,310 So line B, they say 4x is equal to negative 8, and you 64 00:03:20,310 --> 00:03:22,849 might be saying hey, how do I get that into slope-intercept 65 00:03:22,849 --> 00:03:24,039 form, I don't see a y. 66 00:03:24,039 --> 00:03:27,189 And the answer is you won't be able to because you this can't 67 00:03:27,189 --> 00:03:29,900 be put into slope-intercept form, but we can simplify it. 68 00:03:29,900 --> 00:03:33,240 So let's divide both sides of this equation by 4. 69 00:03:33,240 --> 00:03:36,060 So you divide both sides of this equation by 4. 70 00:03:36,060 --> 00:03:40,680 And you get x is equal to negative 2. 71 00:03:40,680 --> 00:03:43,520 So this just means, I don't care what your y is, x is just 72 00:03:43,520 --> 00:03:46,189 always going to be equal to negative 2. 73 00:03:46,189 --> 00:03:49,109 So x is equal to negative 2 is right there, negative 1, 74 00:03:49,110 --> 00:03:51,850 negative 2, and x is just always going to be equal to 75 00:03:51,849 --> 00:03:59,620 negative 2 in both directions. 76 00:03:59,620 --> 00:04:02,180 And this is the x-axis, that's the y-axis, I 77 00:04:02,180 --> 00:04:03,659 forgot to label them. 78 00:04:03,659 --> 00:04:05,879 Now let's do this last character, 2y is equal to 79 00:04:05,879 --> 00:04:07,629 negative eight. 80 00:04:07,629 --> 00:04:12,310 So line C, we have 2y is equal to negative 8. 81 00:04:12,310 --> 00:04:18,980 We can divide both sides of this equation by 2, and we get 82 00:04:18,980 --> 00:04:22,569 y is equal to negative 4. 83 00:04:22,569 --> 00:04:25,019 So you might say hey, Sal, that doesn't look like this 84 00:04:25,019 --> 00:04:28,129 form, slope-intercept form, but it is. 85 00:04:28,129 --> 00:04:29,579 It's just that the slope is 0. 86 00:04:29,579 --> 00:04:34,959 We can rewrite this as y is equal to 0x minus 4, where the 87 00:04:34,959 --> 00:04:38,259 y-intercept is negative 4 and the slope is 0. 88 00:04:38,259 --> 00:04:47,069 89 00:04:47,069 --> 00:04:49,810 So if you move an arbitrary amount in the x direction, the 90 00:04:49,810 --> 00:04:51,569 y is not going to change, it's just going to 91 00:04:51,569 --> 00:04:52,759 stay at negative 4. 92 00:04:52,759 --> 00:04:54,759 Let me do a little bit neater. 93 00:04:54,759 --> 00:04:59,449 y is just going to stay at negative 4. 94 00:04:59,449 --> 00:05:01,709 Or you can just interpret it as y is equal to negative 4 no 95 00:05:01,709 --> 00:05:03,949 matter what x is. 96 00:05:03,949 --> 00:05:06,490 So then we are done.