# Question Video: Finding the Equation of a Straight Line Represented by a Given Graph Mathematics • 8th Grade

Find the equation of the straight line represented by the graph below in the form of ๐ฆ = ๐๐ฅ + ๐.

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### Video Transcript

Find the equation of the straight line represented by the graph below in the form of ๐ฆ equals ๐๐ฅ plus ๐.

So first of all, when solving this problem, we actually want to look at what form the equation needs to be left in. And that is ๐ฆ equals ๐๐ฅ plus ๐. Well, if weโre actually using the form ๐ฆ equals ๐๐ฅ plus ๐, so this is actually the general form for the equation of a straight line, then the ๐ is actually our slope and the ๐ is our ๐ฆ-intercept. And what this means, this is actually where it crosses the ๐ฆ-axis. So in order to actually find the equation of our line, what weโre gonna start with is actually the slope, and find the slope for the line that weโve got.

Well, to actually help us find the slope, we have a formula. And that says that the slope, so ๐, is equal to ๐ฆ two minus ๐ฆ one over ๐ฅ two minus ๐ฅ one. And these actually are the coordinates of two points on the line. This can also be thought of in another way. And that is the change in ๐ฆ divided by the change in ๐ฅ. Okay, great. So letโs use this to actually find the slope of our line.

Well, first of all, what Iโve done is actually identify the two points that weโve got on our line. We could actually use any two points. But these are good ones to choose because actually theyโre on definite values. So we have negative two, seven and one, negative one. And as I said, you can pick them any point on the line because actually the slope of a line, if itโs a straight line, wonโt change.

So then next, what Iโve done is Iโve actually labeled these points. So Iโve got ๐ฅ one, ๐ฆ one and ๐ฅ two, ๐ฆ two. And Iโve just done this so you can actually see whatโs gonna go into our formula to find the slope. So therefore, we can say that ๐, so our slope, is gonna be equal to negative one, because that was our ๐ฆ two, minus seven. And thatโs because that was our ๐ฆ one. Then, this is divided by one, because that was our ๐ฅ two, minus, and then weโve got negative two. Because that was our ๐ฅ one. So therefore, we can say that our slope is gonna be equal to negative eight over three. And thatโs cause negative one minus seven is negative eight. And one minus negative two is three.

So therefore, weโve now found our slope. The next stage is to actually find our ๐ฆ-intercept. However, if we just look on the graph, we can see where it is. We can see where the ๐ฆ-axis has been crossed. However, as the graph isnโt accurate, so we donโt actually have a smaller scale on our axes. We canโt tell exactly what that ๐ฆ-intercept is going to be. So weโre gonna have to find it using another way.

Well, if we actually rewrite our ๐ฆ equals ๐๐ฅ plus ๐, but this time substitute in our ๐-value, weโre gonna get ๐ฆ is equal to negative eight over three ๐ฅ plus ๐. So now, to actually find ๐, what we can actually do is substitute in the values for one of the points we know. So Iโm gonna start with the point one, negative one. Because we actually have that as one of the points on our line. So therefore, when we actually substitute that in, weโre gonna get negative one, because that was our ๐ฆ-value, is equal to negative eight over three multiplied by one, cause that was our ๐ฅ-value, plus ๐. So then, if we actually add eight over three to each side, weโre gonna get negative one plus eight over three is equal to ๐.

So therefore, we can say that ๐ is gonna be equal to negative one plus two and two-thirds. What Iโve done is I actually changed our fraction into a mixed number. And I did that by actually seeing how many threes go into eight. Well, two. So thatโs gonna be two. And then thereโs two left over. So itโs two and two-thirds. So therefore, we have a value of ๐ thatโs gonna be one and two-thirds or five over three. So what we can do now is actually check back on our graph to see if this is actually sensible.

Well, if we have a look at our graph, well yes, if we see that itโs one and two-thirds of five-thirds, then this actually seems sensible. Because the graph crosses the ๐ฆ-axis actually just below two. So actually, it does look in the correct place. So therefore, if we substitute back in our values for ๐ and ๐, we can say that the equation of the straight line represented by the graph shown is ๐ฆ equals negative eight over three ๐ฅ plus five over three. And this is in the form ๐ฆ equals ๐๐ฅ plus ๐.