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Added: 2026-05-27

[00:03:11]All right. All right. Now drawing 3.

[00:03:42]Okay.

[00:03:49]Why? = x + 3.

[00:03:56]This is the equation given to us.

[00:04:00]All right. All right people. Um [snorts] equations.

[00:04:14]Let me just write a linear linear equations.

[00:04:24]Linear equations.

[00:04:27]You want to deal with linear equations.

[00:04:30]people.

[00:04:42]Grade eight.

[00:04:45]Grade eight.

[00:04:50]Grade eight.

[00:04:52]Grade eight.

[00:05:36]I ain't linear equations.

[00:05:56]Want to deal with the linear equations.

[00:05:59]My people, I'm just waiting for others to join me.

[00:06:10]Can I answer this person? Um, let me answer someone.

[00:06:22]Guys, I'm back. I'm back again, guys.

[00:06:26]I'm back. I'm back again.

[00:06:29]I'm just waiting for others to join. You know, I join in so that um I join some.

[00:07:01]Okay, I'm just waiting for others to join. Thank you.

[00:08:34]Okay.

[00:08:40]Okay.

[00:08:44]And check something and check something.

[00:08:48]So now we can start uh engaging about this uh linear equation people.

[00:08:54]We can start engaging about this linear equations.

[00:09:14]Okay, let me start. Let me start. Um hey guys a linear equation a linear equation we are talking about um we are talking about an equation whose graph is a linear okay whose graph is what is a linear so it's a line I mean whose graph is a line so let me just uh define Find this. I'm saying this is an equation equation whose graph is a line.

[00:10:05]A line a straight line. Okay. So a linear equations or a linear equation is an equation whose graph is what? Is a line. So in this case we want to talk about this linear graphs I believe right. So with the linear graphs if ever they saying complete the table and graph the linear equation.

[00:10:37]You complete the table and then you graph the linear equation. So you will be given um a linear equation uh which is y = to x + 3. Okay. So in this case now you know that x x it's your what? It's your input.

[00:11:01]X we refer to the input inputs x values but y is the output.

[00:11:10]Okay. So x and uh x and input y is the what is the output. So in this case we know that this equation y = x + 3 y= x + 3. This is a rule.

[00:11:30]This is a rule diagram right and then you have to find the the input at some point you have to find the output. So, so a linear equation we're talking about an equation whose graph is a line and then you will be given the the equation in the form y = x + 3 or in the form of y = m x + c. We shall talk about that later on. But equation standard form y= mx + c standard form equation where m is the slope or the gradient of the graph. Right? But c is the constant number.

[00:12:26]So y = x + 3 input and the output and the one= rule. So in this case they will say complete and graph the linear equation. So in this case you are going to complete this table. To complete this table you have your x's here. So you're going to say y= where there is x3 + 3 as the output. And then y= - 2 - 2 + 3 x.

[00:13:51]1 this -1 + 3 and the answer will be 2.

[00:14:04]We move in that order. Again we are saying y it= to where there is x we replace by zero. So it will be 0 + 3 which is equals to 3. It means here we have three.

[00:14:22]You replace x by one. It's y. It = to 1 + 3. And the answer is four. It means here we have what? Four.

[00:14:36]We move to two. We see y it equals to where there is x. You replace by what?

[00:14:42]By two. So it will be 2 + 3 and the answer is five.

[00:14:50]Move to the last one. X. You replace X by 3.

[00:14:57]Replace X by 3.

[00:15:00]Let's replace X by 3. It will be Y. It is equals to 3 + 3 which is equals to six.

[00:15:09]So the last one here we got six. Right?

[00:15:12]So the output I said that these are the input inputs and these are the what are the outputs. Okay. So now okay graph right in the form of a linear equation. So uh draw a graph drawing the cartisian plane this our cartian plane right and then we draw something like this drawing cartian plane and the horizontal line the horizontal line it represent what it represent x and the vertical line it represent what y values X is 0. Y is Z.

[00:16:49]1 2 3 4 5 6 So it will be 6 5 4 3 2 1 Same applies here -1 - 2 -3 -4 - 5 Just like that -1 - 2 -3 -4 - 5 in that order you can just proce proceed with the negatives up to the negative infinity if ever. So there it will be 1 2 3 -1 -2 -3 -4 -5 up to infinite. Right? So this can be 1 2 3 4 5 6 up to um positive infinity. So we have something like this. So plane right -3 and 0 is a point -2 and one is a point just like that. This a point a point a point a point a point.

[00:18:17]So information US.

[00:18:36]Okay.

[00:18:47]This is the origin. Okay. This is the origin of the graph.

[00:18:56]This is the origin. Okay. the origin O and Z Y X. So it's minus it's 3 andus.

[00:19:17]Okay.

[00:19:19]And then we are done with number one.

[00:19:26]Number two and one x values xus2us and one. So this is the point we're talking about and 2 -1 and 2 - xt just like that and X output output.

[00:20:30]One and four. One and four. One X positive X values.

[00:20:47]Okay.

[00:20:51]Two and five.

[00:21:03]Three.

[00:21:05]Three. X. Three. X.

[00:21:27]a straight line. Let me draw a straight line passing through these points.

[00:21:37]Okay.

[00:21:40]Straight line. This is our straight line. What graph?

[00:21:57]Complete complete the table and draw the linear what equation.

[00:22:18]All these points, all these points on a line is a solution of the graph equation. Okay, let's move to example number two. This was example number one.

[00:22:32]Let's move to example number two.

[00:22:36]Example number two.

[00:22:40]y it = to 2x - 1.

[00:22:53]You have been given this uh table for x and y.

[00:23:01]You are given this table for x and y guys.

[00:23:09]So you know x you know y let me start with -2 -1 0 1 2 okay so this what we have now this what we have a table this is the table we have okay fine You can just end here. So now very complete complete complete the table and draw a linear you have to draw a linear a linear equation. Okay.

[00:24:05]So basically we are going to use we are going to use the very same procedure.

[00:24:15]We complete the table and we draw a linear equation or a line which represent the linear equation. So in this case so y= y= 2 open 2 - 2 -1 it's -5 it's -5 5 x - 1. So the answer in this case will do what?

[00:25:11]It's -3 by calculate x is 0 is 2 open bracket 0 - 1 2 * 0 2 * 0 is 0 - 1 is minus one.

[00:25:28]Okay.

[00:25:31]Replace replace one replace x1. So it's 2 * 1 - 1 which is equals to 1us.

[00:25:50]Oh, it's positive2. Sorry.

[00:25:53]2 - 1.

[00:25:59]We getting what? It's 2 * 2 4 - 1 is 3.

[00:26:16]Car 0 - one car one in a one sorry and then car two in a three done.

[00:26:27]So now we draw graph here. Let's draw our graph.

[00:26:32]Let's draw our graph.

[00:26:36]We are drawing our graph. Now we want to draw our graph here.

[00:26:45]We're drawing our graph. This is y. This is x. Okay.

[00:26:52]-1 - 2 - 3 -4 - 5. Just like that. Okay.

[00:26:59]So, this will be 1 -1 - 2 - 3 - 4 - 5.

[00:27:10]It's 1 2 3 4 and 5.

[00:27:17]1 2 3 4 and 5.

[00:27:25]Okay.

[00:27:28]So now Y output minus money five.

[00:27:48]So this is the point.

[00:27:51]Okay.

[00:27:54]You go - 2 Oh, -1 - 3 -1 x - 3 y XG calling Q two point People [snorts] say join. We need to join our points now.

[00:29:02]So it's easy every time.

[00:29:18]X and Y X and Y X and Y just like that.

[00:29:22]Okay.

[00:29:26]Now we move to the horizontal line. Let me just write horizontal line. We're moving to the horizontal horizontal line.

[00:29:48]The other one it will be a vertical line. Okay. So let's talk about the horizontal and the vertical line. Right?

[00:29:59]For horizontal line a horizontal line it's a line. A horizontal line will have an equation.

[00:30:10]This will will have an equation.

[00:30:17]Equation y it is equals to be. So in this case b this b it represent a number.

[00:30:29]The value of B represent what will be the point where line crosses Yaxis.

[00:30:38]B will be what? B will be will be the point [clears throat] where the line where the line does what? where the line crosses the y axis.

[00:31:04]Okay.

[00:31:08]Cartesian plane like this.

[00:31:11]You are given a cartian plane like this one that saying this y and x. All right.

[00:31:21]You are given an a cartian plane like this one. So that's saying you need to draw the graph of y it is = to - 2.

[00:31:36]So here you'll be given 1 2 1 2 - 1 - 2 -1 - 2. So the line cross the yaxis horizontal line our horizontal what lineal y=2al Y2 passing through -2. This is our graph.

[00:32:41]Y= -2 Y= 1 something horizontal lineal lineal line drawraph A this is our graph passing through one and then you indicate this our graph y= 1. So this is how you draw a graph of a horizontal line in the form y= b where line crosses the y ais b represent a number. So this the number that we're talking about vertical line vertical line A vertical line will have will have an equation yx sorry sorry x x I wanted to say x okay let me do this we will we have an equation x it is equals to a where a it represent the oh it represent the point where the line crosses the x-axis A represent the point.

[00:34:36]The point where the line crosses the x axis.

[00:34:46]Okay. So it represent the point where the line crosses the what? The xaxis.

[00:34:55]cartesian plane like this.

[00:35:00]This is your cartian plane and that's saying this y and this x.

[00:35:08]Okay. So here you have -1 -2 -3 -4.

[00:35:15]This one 2 3 4.

[00:35:22]Okay. 1 2 3 4.

[00:35:32]All right.

[00:35:34]Vertical line. A vertical line will have an equation x= to a where a represent the point where the line crosses the x-axis.

[00:35:47]So in this case eg if you are given x it= to3 graph3 x is this point here3 draw a vertical line draw a vertical line passing through that point.

[00:36:13]Let me use the right one. This is the point I'm talking about. Okay, with this point now a vertical line x= 3 or x = 2.

[00:36:42]Draw a vertical line passing through that two.

[00:36:55]So this graph represent x= to Come back. Lesson one.

[00:37:28]Okay.

[00:37:30]Homework.

[00:37:33]Homework.

[00:37:36]Homework.

[00:37:39]Homework.

[00:37:44]Homework.

[00:37:48]Homework. You are given an equation like this.

[00:37:52]Let me show you the equation.

[00:37:56]Complete. Let me write it here.

[00:38:02]Complete the table and graph the linear equation.

[00:38:21]If they say graph the linear equation they mean draw or represent the table in the cartian plane in the form of a line.

[00:38:32]So you'll be given a table like this.

[00:38:37]This will be your table.

[00:38:41]This will be a table. Right?

[00:38:44]And then from this table you know that you'll be given x x and y.

[00:38:52]So yeah, let's use minus - - 2 or let me say -3 - 2 - 1= 0 1 2 and 3. So you have to find the the the output right and the equation is y it= to 2 / 3x + 4.

[00:39:26]So this is the equation.

[00:39:30]This is the equation.

[00:39:41]text WhatsApp.

[00:39:45]0 66 372 68 55 5. So this is the WhatsApp number.

[00:40:02]You can use this WhatsApp number, right?

[00:40:05]So that at least the linear graph. Okay.

[00:40:17]Right.

[00:40:23]the relationship between proportional relationships and line relationships and then you also find and interpret the slope of proportional relationship.

[00:40:38]Graph the proportional relationship compare the proportional relationships.

[00:40:43]So some of the things uh we did not complete for today. But Cool.