WEBVTT 00:00:00.440 --> 00:00:03.480 Write the equation represented by the graph shown. 00:00:03.920 --> 00:00:08.880 Give your answer in the form ๐‘ฆ minus ๐‘Ž equals ๐‘š ๐‘ฅ minus ๐‘. 00:00:09.600 --> 00:00:15.240 Right, so to solve this problem and find the equation thatโ€™s represented by this graph, weโ€™re gonna have to use this form thatโ€™s given here. 00:00:15.560 --> 00:00:20.560 And this is known as the point-slope form or the point-slope equation. 00:00:21.000 --> 00:00:23.120 Letโ€™s break down what each part of it actually means. 00:00:23.600 --> 00:00:25.480 Well, first of all, we have our ๐‘Ž and ๐‘. 00:00:25.720 --> 00:00:27.680 And these are actually coordinates from a point that you choose. 00:00:27.920 --> 00:00:30.280 And in this case, weโ€™ve actually highlighted that point on the graph. 00:00:30.840 --> 00:00:38.000 Okay, so we now know that ๐‘Ž is going to be our ๐‘ฆ-coordinate and ๐‘ is going to be the ๐‘ฅ-coordinate of that point thatโ€™s highlighted. 00:00:38.560 --> 00:00:40.640 Right, next part weโ€™re gonna have a look at is the ๐‘š. 00:00:40.920 --> 00:00:42.880 And the ๐‘š is the slope of the graph. 00:00:43.280 --> 00:00:45.920 And this is the slope of the graph between any two points on that straight line. 00:00:46.360 --> 00:00:49.960 Because itโ€™s a straight line, the slope will remain constant. 00:00:50.600 --> 00:00:50.960 Great! 00:00:51.400 --> 00:00:55.120 Now we can get on with solving the problem and finding the equation. 00:00:55.480 --> 00:00:59.320 So in order to do that, weโ€™re gonna start by finding ๐‘š, so the slope of the graph. 00:01:00.000 --> 00:01:09.440 To do that, weโ€™ve got an equation, which weโ€™ll put on the right-hand side, which is the ๐‘š is equal to ๐‘ฆ two minus ๐‘ฆ one over ๐‘ฅ two minus ๐‘ฅ one. 00:01:09.920 --> 00:01:13.800 So this basically means this is the change in ๐‘ฆ divided by the change in ๐‘ฅ. 00:01:14.160 --> 00:01:19.000 In order to enable us to do this, we need to look at another point on our graph, which Iโ€™ve circled here. 00:01:19.520 --> 00:01:21.040 And when youโ€™re choosing which point to use, it doesnโ€™t really matter. 00:01:21.320 --> 00:01:28.240 But Iโ€™d say to make it easy for yourself always choose a point thatโ€™s very definitely on an ๐‘ฅ-coordinate and a ๐‘ฆ-coordinate, okay? 00:01:28.760 --> 00:01:31.960 And Iโ€™ve just highlighted onto the graph the change in ๐‘ฆ and the change in ๐‘ฅ. 00:01:32.320 --> 00:01:35.800 So that means how much it goes up and how much it goes along. 00:01:36.360 --> 00:01:38.480 Okay, so weโ€™re now going to put values into the formula. 00:01:38.880 --> 00:01:43.040 But to do that, we need to know the coordinates of the two points weโ€™ve chosen. 00:01:43.280 --> 00:01:45.000 I have labelled them ๐‘Ž and ๐‘. 00:01:45.360 --> 00:01:51.040 So point ๐‘Ž is minus two, six and point ๐‘ is two, eight. 00:01:51.400 --> 00:01:53.400 Right, and weโ€™re now going to put this into our formula. 00:01:53.880 --> 00:01:59.600 And to enable us to do that, Iโ€™ve actually just labelled them ๐‘ฅ one, ๐‘ฆ one; ๐‘ฅ two and ๐‘ฆ two. 00:02:00.120 --> 00:02:06.680 And this gives us the equation ๐‘š is equal to ๐‘ฅ [eight] minus six divided by two minus negative two. 00:02:07.360 --> 00:02:14.040 Right, we now simplify this, which will give us two divided by- now be careful here again with negative numbers. 00:02:14.480 --> 00:02:21.000 Two minus negative two, this turns to a plus when add. 00:02:21.360 --> 00:02:23.320 So weโ€™re gonna get two divided by four. 00:02:23.840 --> 00:02:25.200 So we can simplify even further. 00:02:25.440 --> 00:02:27.080 And it gives us ๐‘š. 00:02:27.600 --> 00:02:29.720 So our slope is equal to a half. 00:02:30.320 --> 00:02:30.640 Great! 00:02:31.240 --> 00:02:32.600 So weโ€™ve now found ๐‘š. 00:02:33.240 --> 00:02:33.680 Fantastic! 00:02:34.080 --> 00:02:41.040 Now that weโ€™ve found the slope, we can actually use this to write the equation of this graph in the point-slope form. 00:02:41.600 --> 00:02:43.480 First of all, we start with ๐‘ฆ minus ๐‘Ž. 00:02:43.800 --> 00:02:48.560 Well, ๐‘Ž is going to be the ๐‘ฆ-coordinate of the point thatโ€™s actually highlighted on the graph, which is point ๐‘Ž. 00:02:48.560 --> 00:02:49.920 So thatโ€™s going to be equal to six. 00:02:50.120 --> 00:02:51.200 Then, weโ€™re gonna open the parentheses. 00:02:51.400 --> 00:02:59.080 And itโ€™s gonna be ๐‘ฅ minus ๐‘, which in this case is gonna be our ๐‘ฅ-value of the point that weโ€™ve highlighted, which is negative two. 00:02:59.680 --> 00:03:05.600 So this gives us the equation ๐‘ฆ minus six equals a half ๐‘ฅ minus negative two. 00:03:06.400 --> 00:03:13.920 Okay, we can still simplify this a little bit further because obviously ๐‘ฅ minus negative two, this will turn positive. 00:03:14.720 --> 00:03:21.480 So we can say weโ€™ve got the final equation ๐‘ฆ minus six equals a half ๐‘ฅ plus two. 00:03:21.880 --> 00:03:23.560 And thatโ€™s in the point-slope form. 00:03:24.320 --> 00:03:24.680 Great! 00:03:25.120 --> 00:03:35.040 So a quick recap of what we did, first of all, we found the slope using the equation ๐‘š is equal to ๐‘ฆ two minus ๐‘ฆ one divided by ๐‘ฅ two minus ๐‘ฅ one. 00:03:35.640 --> 00:03:52.560 And once we did that, we actually then put that into our point-slope form along with the values for ๐‘Ž and ๐‘, which were the ๐‘ฅ- and ๐‘ฆ-coordinate of the point highlighted on the graph, which gave us our final equation of ๐‘ฆ minus six equals a half ๐‘ฅ plus two.