What is an integer?

Complete the following sentence: On a horizontal line the..............

Question 2

Which integer values can y be for the inequality shown above?

Which of the following inequalities covers the following integer values of x?    -1, 0, 1, 2, 3, 4?

Which of the following coordinates satisfies the inequalities; -2 < x < 3 and -5 < y < 3?

﻿Hello, and welcome to another video. I am Mr. Maseko and I'll be going through this lesson with you today. In today's lesson, we'll be looking at naming straight line graphs. Now, before you begin this lesson, please make sure you have a pen, pencil, ruler, and your notebook. If you don't have those things, pause the video here and go get them now. Okay, now that you have those things, let's get on with today's lesson. The first thing that I want you guys to try and do is to answer the question that's on the board. Pause the video hit and give this a go. Okay. Now let's see what we have come up with. Now, the first question is write three different coordinates that each student might be thinking of. Starting with Javier. He says in his coordinate, the Y ordinate is three greater than the X ordinate. So what could he be thinking of? Okay. Yes, he could be thinking of the coordinate one, four, because four is three greater that one. Another one. What else would you be thinking of? Yes, he could be thinking of the coordinate two, five, or he could also be thinking of the coordinates zero, three. Really well done if you came up with any of those, and I'm sure the answers you came up with are also equally as right. The next one. Yasmin says, "In my coordinate, the Y ordinate is double the X." So what coordinates could Yasmin be thinking of? Okay. One, two. One, two sound good. One, two, because two is double one. Another one, well, if it's all in doubles, we could also say three, six, 'cause six is double three. Another one we could say four, eight. Okay. Did you come up with any more? Well done. As long as your Y ordinate is double your X, you are also correct. The next one for Zaki. He says his Y ordinate is always 10, or his Y ordinate is 10. Well, for whatever coordinate he's thinking of his, his Y ordinate is 10? Does he tell us what the X is? No, he just said Y is 10? So we can say that the X can be anything at all. So any coordinates that you came up with with a Y of 10 would have been correct for Zaki. Really well done for getting through this. Now, getting on to the main part of today's lesson. Here's what I want you to do. Plot the coordinates that's you came up with onto the coordinate grid, and see what you notice. And now think back to the second question in the try it now, which was is it possible for two students to be thinking of the same coordinates? See if this helps you figure out whether it is possible or not. So pause the video here and try plotting your coordinates onto this grid and see what you notice. Okay. So what did you notice when you plotted your coordinates? What is it? Huh, did you notice that for all of Javier's coordinates that you came up with, they all lie on this green line? Well, let's see. The coordinate one four, one across and four up. Yes, that's on the green line. The coordinate zero, three. That's also on the green line. The quote, an eight, 11. Huh, that's all in the green line. So when we plot coordinates using the same rule, what can we say? They form a straight line. So anytime you or coordinates using the rules that we've been given in this instance, they seem to plot a straight line. Now later on, you'll figure out that there are other rules that we can use to plot coordinates that don't form straight lines like this, but that will come later on. But for the rules that we're going to be using, the coordinates that we are going to be plotting will all form straight lines. And you should have also noticed that all your coordinates for Yasmin, those are all on the purple line, and all your coordinates for Zaki, those are all on the orange line. Now, if you noticed this, really, really well done. Now, what did you come up with for the question? Is it possible for two students to be thinking of the same coordinates? If you said yes, you are correct, because if you look at it, you can see that there are points where the lines cross each other, and the coordinate where the lines cross, that coordinate lies on both lines. So you should look at the coordinates three, six. This coordinates satisfies two rules. The Y ordinate is three greater than the X ordinate, which was Javier's rule. And the Y ordinate is double the X ordinate, which was Yasmin's rule. So it is possible, and by plotting straight lines like this, we can find coordinates that lie on more than one line. Now we want to be able to plot straight lines, but we do not want to be using these bulky rules in order to plot them. Listen, as mathematicians, we like to make our lives simple, the simpler, the better. Now I'm going to show you one way that you can simplify writing the rule for a straight line, but there are many other ways that you could write them. But the way I choose is what we're going to be using for this sequence of lessons. So if you look at it, we are trying to find Y ordinates. So we can say that to find our Y ordinate, well, what did Javier say we should do? Well, Javier said to find our Y ordinate we have to take our exponent and add three, 'cause a Y ordinate is three greater than the X, ordinate. So, we take our Y ordinate, to find it, we take our X, and then we add three. So now look at this. This is a much simpler way of writing that bulky sentence. Can you try this for the other two students? Can you simplify what they've said in words and write it in the same form that I wrote Javier's rule? Pause the video here and give it a go. Okay, so what did you come up with? Well, for Yasmin, you should have come up with Y is equal to two X because the Y ordinate is always double the X ordinate. So Y is equal to, is the same as two X. And then for Zaki, well, he just says his Y ordinate is 10. Is 10, so his Y ordinate is equal to 10. So no matter where you are on Zaki's line, the Y ordinate will always be 10. So really well done if you came up with those rules. Like I said, there are different ways that we could write this, like for example, and if we change colour here, we could write that first rule as being the X ordinate is equal to the Y ordinate take away three. Now that's an equally valid way of writing that rule. Or we could have said that Y ordinate take away the X ordinate is equal to three, and that's also equally as valid. But the notation that we're going to use, the form for writing those rules that we're going to use, as I said, is when Y is equal to something, 'cause we're trying to find out Y ordinates using our X ordinates, and we manipulate them in a certain way. So here's what I want you to do next. Onto the graph that you have. Can you come up with three or four coordinates that satisfy Antoni's line, and plot them onto the grid? And then also, after you've done that, label Antoni's line using our simplified notation, Pause the video here and give this a go. Okay, so what you should have come up with is four coordinates. So what coordinates could you come up with? Well, you could have come up with if the Y ordinates are one less than the X, you could've come up with three, two; five, four; seven, six; nine, eight. For all those coordinates, the Y is one less than the X. And then you'd have plotted this on the coordinate grid and then joined those with a straight line. Make sure you're using a ruler to plot your straight lines. And now to label this, you should have come up with Y being equal to the X ordinate, take away one. And really well done if you came up with this. So now pause the video here and give that independent task a go. So what did we come up with for independent task? Well, I will just give you one coordinates for each of those lines. So for Y equals three X, you could have come out the coordinates two, six. As long as your coordinate, the Y, is three times the X, your coordinates are correct. For Y equals 10 take away X, well, you could have done three, seven because 10 take away three gives you seven. For Y equals X plus four, you could have done four, eight because for add four gives you eight; and then complete this coordinates for the line, Y equals 12 minus X. What X is one? 12 take away one. That gives you 11. One X is eight, 12 take away eight. That gives you four. When Y is 12, so you can say 12 is equal to 12 take away X or 12 take away something gives you 12. So then this something that we take away has to be equal to, 12 take away Y gives you 12, or 12 take away zero. So X would have to be zero. And then when X is negative one, 12 take away negative one, or that would be equal to the 13. When X is negative one, Y is 13. And three lines with a coordinate two, six. Well, we've we have one already that's on there, which is Y is equal to three X because six is three times two. What else could you have come up with? Well, you could've come up with Y being equal to X add four 'cause two add four gives you six. What did you come up with? Well, you could have done Y is equal to two X add four. Not two X add four. Is that correct? No, it isn't because two times two is four. To get to six, we don't add four. We have to add, you got it. You have to add two. Really well done for spotting by mistake. Now what I want you to do is have a go at this Explore task. Pause the video here if you don't want any support doing this. Okay, so let me give you a clue how to do this if you're stuck. So we've got two lines, Y equals two X, and Y equals 15 minutes X, and that coordinate five, 10 lies on both those lines. 'Cause if we look at it, two times five gives you 10, and 15 take away five also gives you 10. So both those lines have the coordinate five, 10 in them. What other line could have the coordinate five, 10 in them? Well, we could do Y is equal to three X, or three times five is 15. That doesn't give us 10. So what do we do to 15 to get 10? Well, we can take away five. Okay. Try this now and see what you come up with. Okay, now that you've given this a go, what lines did you come up with? Well, another simpler one that you could've come up with is Y is equal to X add five. What else did you come up with? Well, you could have done Y is equal to four X or four X plus four times five is 20. To get to 10, I take away 10. There are many more lines you could have come up with, and I look forward to seeing what you have come up with for this question. And lines for these equations that I hear, well, zero, zero, both are the same, so you can say Y is equal to X, three, nine could be Y is equal to three X, and four, negative four could be Y is equal to X take away eight. Now, if you've come up with different lines and you want to share your work, ask your parents or carers to share your work with Oak, and you can tag it on Twitter at OakNational and hashtag LearnWithOak. Thank you for participating in this video, and I hope to see you again next time. Bye for now.

John says, "In my line, all my y-ordinates are triple my x-ordinates". Tick the equation that represents John's line.

Jenny says, "In my line, all my y-ordinates are 5 less than my x-ordinates". Tick the equation that represents Jenny's line.

Which of the following lines does the point (2,6) lie on?

Which of the following lines does the point (3,-6) lie on?

Which of the following coordinates lies on the line y=2x-1

Naming straight line graphs

In this lesson, we will be looking at plotting coordinates onto a grid and simple notation for labelling straight line graphs.

Maths

Y8 Maths

Key Stage 3

Year 8

Linear graphs

Algebra

THEME

UNIT

Coordinates recap

Horizontal and vertical lines

Inequalities

Inequalities (Part 2)

Linear and non-linear graphs

Gradient 1

Gradient (Part 2)

Comparing gradients

y = mx + c

Equations of lines

Equivalent lines

Which of the following is an example of a vertical line

Which of the following coordinates lies on the line y = 5

What is the following inequality saying? -3<x<5

What is the gradient of the green line?

Which of the following lines has the same gradient as the line y = 4 - 2x?

Which of the following coordinates is the same distance from the coordinate (0,0) as (6,3)

Which of these coordinates is in the middle of (6,4) and (10,8)

What is a linear graph?

What is the coordinate of the y-intercept for the line y = 2x + 7?

What is the gradient of the line that goes through the point (3,4) and (4,1)?

Lesson overview:Naming straight line graphs

Core Content

Linear graphs: