A line goes through the points ( -1, 6 ) and ( 5, -4 ). What is the equation of the note ? Let ‘s merely try to visualize this. So that is my ten axis. And you do n’t have to draw it to do this trouble but it always help to visualize That is my y bloc. And the beginning point is ( -1,6 ) so ( -1, 6 ). sol negative 1 coma, 1, 2, 3, 4 ,5 6. So it ‘s this point, rigth over there, it ‘s ( -1, 6 ). And the other degree is ( 5, -4 ). sol 1, 2, 3, 4, 5. And we go down 4, then 1, 2, 3, 4 So it ‘s correct over there. So the line connects them will looks something like this. Line will draw a roughly approximation. I can draw a straight than that. I will draw a dotted line possibly Easier do dotted line. So the line will looks something like that. So get ‘s find its equality. then good position to start is we can find its slope. Remember, we want, we can find the equation yttrium is adequate to mx plus b. This is the slope-intercept form where thousand is the slope and boron is the y-intercept. We can first try to solve for m. We can find the gradient of this course. So meter, or the slope is the change in y over the change in ten. Or, we can view it as the yttrium value of our end point minus the yttrium value of our starting point over the x-value of our end orient minus the x-value of our starting point. Let me make that clear. therefore this is equal to change in yttrium over transfer in x wich is the same thing as resurrect over run wich is the same thing as the y-value of your ending point minus the y-value of your starting point. This is the lapp demand thing as change in y and that over the x value of your ending point minus the x-value of your starting point This is the demand same thing as change in adam. And you fair have to pick one of these as the begin orient and one as the ending point. So let ‘s precisely make this over here our starting point and make that our ending point. So what is our change in y ? So our transfer in y, to go we started at yttrium is adequate to six, we started at yttrium is peer to 6. And we go down all the way to y is peer to minus 4 so this is rigth hera, that is our change in y You can look at the graph and say, oh, if I start at 6 and I go to negative 4 I went down 10. or if you just want to use this formula here it will give you the lapp thing We finished at negative 4, we finished at negative 4 and from that we want to subtract, we want to subtract 6. This right hera is y2, our ending y and this is our beginning yttrium This is y1. so y2, veto 4 minus y1, 6. or damaging 4 subtraction 6. That is peer to negative 10. And all it does is tell us the change in yttrium you go from this point to that charge We have to go down, our resurrect is negative we have to go down 10. That ‘s where the damaging 10 comes from. now we just have to find our variety in adam. So we can look at this graph over here. We started at x is peer to negative 1 and we go all the way to x is equal to 5. So we started at x is adequate to negative 1, and we go all the way to x is peer to 5. So it takes us one to go to zero and then five more. So are change in adam is 6. You can look at that visually there or you can use this formula same claim idea, our ending x-value, our ending x-value is 5 and our starting x-value is negative 1. 5 minus minus 1. 5 minus negative 1 is the like thing as 5 plus 1. So it is 6. so our slope here is negative 10 over 6. wich is the claim same thing as damaging 5 thirds. as negative 5 over 3 I divided the numerator and the denominator by 2. So we now know our equality will be y is equal to negative 5 thirds, that ‘s our slope, x plus barn. So we however need to solve for y-intercept to get our equation. And to do that, we can use the data that we know in fact we have several points of information We can use the fact that the agate line goes through the degree ( -1,6 ) you could use the other point american samoa well. We know that when is equal to damaging 1, So y is eqaul to 6. thus y is equal to six when ten is equal to negative 1 indeed veto 5 thirds times ten, when x is equal to negative 1 y is equal to 6. So we literally good substitute this x and yttrium value back into this and know we can solve for boron. So lease ‘s see, this negative 1 times veto 5 thirds. So we have 6 is equal to positive five thirds plus boron. And now we can subtract 5 thirds from both sides of this equality. so we have subtracted the left hand side. From the left handside and subtracted from the rigth handside And then we get, what ‘s 6 minus 5 thirds. So that ‘s going to be, let me do it over here We take a common denominator. thus 6 is the lapp thing as Let ‘s do it over hera. so 6 minus 5 over 3 is the same matter as 6 is the same thing as 18 over 3 minus 5 over 3 6 is 18 over 3. And this is just 13 over 3. And this is merely 13 over 3. And then of class, these cancel out. So we get b-complex vitamin is equal to 13 thirds. So we are done. We know We know the gradient and we know the y-intercept. The equation of our line is y is equal to negative 5 thirds ten plus our y-intercept which is 13 which is 13 over 3. And we can write these as blend numbers. if it ‘s easier to visualize. 13 over 3 is four and 1 thirds. so this y-intercept correct over here. this y-intercept right field over hera. That ‘s 0 coma 13 over 3 or 0 coma 4 and 1 thirds. And even with my very roughly drawn diagram it those looks like this. And the slope veto 5 thirds that ‘s the same thing as negative 1 and 2 thirds. You can see here the slope is down because the slope is negative. It ‘s a little bite steeper than a slope of 1. It ‘s not quite a negative 2. It ‘s negative 1 and 2 thirds. if you write this as a minus, as a assorted number. therefore, hopefully, you found that entertaining.