![]() ![]() ![]() So the line will looks something like that. I will draw a dotted line maybe Easier do dotted line. So the line connects them will looks something like this. And we go down 4, So 1, 2, 3, 4 So it's right over there. So it's this point, rigth over there, it's (-1, 6). And the first point is (-1,6) So (-1, 6). And you don't have to draw it to do this problem but it always help to visualize That is my y axis. What is the equation of the line? Let's just try to visualize this. This means that it is an ENTIRELY different point on the line, as the change in y over change in x is equal to -10/6, or -5/3.Ī line goes through the points (-1, 6) and (5, -4). 69/15 = x And lastly, dividing -69 by 15 gives us.Īlright, so we know that when y is equal to -10, then x is equal to -4.6. 23/3 * 3/5 = x And multiplying this out will give us. 23/3 / 5/3 = x As for the left hand side, we know that dividing by a fraction is the same thing as multiplying by it's reciprocal, so it becomes 23/3 / 5/3 = 5/3x / 5/3 The right hand side cancels out 23/3 = 5/3x, so now we divide both sides by 5/3 So first, we subtract 13/3 from both sides. 10 = 5/3x + 13/3 and from this, we can solve for x in this situation. ![]() Now to compare this to when y equal to -10, we would have this: We also know from the given points that when y equals 6, x is equal to -1. The change in y over the change in x equals out to -10/6, or -5/3. This is seen when you compare the points and the slope. However if Sal were to use -10, the x value he would have to be different. If -10 from the slope were to be a valid option for a point in this equation, that means that the change in x would also have to be the accompanying point on the line to go with the change in y. He could not use -10, because -10 isn't necessarily a point on the line, because it's the change in y. It worked out.He used 6 because it was one of the points for y on the line. So it is, negative 14x plus 21y is equal to 12. Of them the way I did in that previous example. If there was a common factorįor all three of these numbers then I would divide all And 21 and 12 are divisibleīy three but 14 isn't. But all of these aren'tĭivisible by the same number. 12 is divisible by two, six, three, four. Now let's see, am I done? Do these share any, do 14, 21, and 12 share any common factors? Let's see, 14 is divisibleīy two and seven. Let's see and I subtractedġ4x to get rid of this. So on the left hand side I have negative 14x plus 21y. Then what am I left with? Let me give myself a I can't just do it on the right hand side I have to do it on the So I wanna get thisġ4x onto the left side. And now I wanna get all the X's and Y's on one side. Three times seven of course isĢ1, we just figured that out. ![]() So this is going to be multiplied by three and multiplied by seven. Three and I multiply by seven, I have to do that to this side as well. So we start with Y is equal to 2/3x plus 4/7. So if you multiply threeĪnd you multiply by seven. Rid of the fractions is to multiple by threeĪnd to multiply by seven. The first thing you could try to do is well let's get rid ofĪll of these fractions. So the first thing I would wanna do is, well there's a bunch of ways Because there's obviously aīunch of forms in this way. That they're asking for and probably because it's just easier for the site to know that You get 2x, divide this by two you'll get plus y is equal to 5. Divide them all by twoĪnd then you would get two so you divide this by two. Number, and this number are all divisible by two. So if we got to the point of say 4x plus 2y is equal to 10, well this number, and this That just means that A, B,Īnd C in the standard form they want need to be integers. Which means all numbers must be integers that do not share a commonįactor other than one. And that extra text they were saying, the equation must be simplified. Which would be the form Ax plus By is equal to C. But we wanna write this in standard form. Out what the slope and what the Y intercept It's written in the form Y is equal to mx plus b, where m in this case is 2/3 and b is 4/7. So the way that it's written right now, this is slope intercept form. The equation must be simplified, which means all numbers must be integers that do not share a commonįactor other than one. Rewrite Y is equal to 2/3x plus 4/7 in standard form. ![]()
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