![]() ![]() So it would be X equalsįour, Y equals nine, which we have right up there, and then the slope is right over here, it's negative four. This line with things that make both sides of Parenthesis like this, but we could figure out the point from this point-slope form. We have the point, sometimes they even put And this right over here is our classic, this right over here is ourĬlassic point-slope form. So we get Y minus 9, we get Y minus nine is equal to our slope, negative four times X minus four. To do that, we just multiplyīoth sides times X minus four. And we're not in point-slope form or classic point-slope form just yet. And the slope betweenĪny two points on a line are going to have to be constant. This is going to be the slopeīetween any XY on this line and this point right over here. So if we find the difference between that Y and this Y, and nine, and it's over the difference between some X on the line and this X, and four. Y that sits on this line and if we find the differenceīetween that Y and, let's focus on this point up here. We know that the slope betweenĪny two points on this line is going to be negative four. It is I always like to just take it straight from theĭefinition of what slope is. So now that we have a, now that we know the slope and we know a point, we know a, we actually know two points on the line, we can express this in point-slope form. ![]() And so what's your slope? Change in Y over change in X. And what was your change in X? Again to get to this point? Well, your change in X is positive two. So your change in Y isĮqual to negative eight. This point your change in Y, your change in Y is you went down eight. And you could have even done it visually. We started at X equals four, so our change in X is six minus four, which is equal to two. So we end up at X equals six and we started at X equals four. And what's our change in X? Well we go from X equalsįour to X equals six. So this is going to be equal to, this is going to beĮqual to negative eight. We have a negative eight change in Y, which makes sense. So we started at Y equals nine, we finish at Y equals one, our change in Y is going Point and we go to that point, then our change in Y, goingįrom this point to that point is going to be, it's going to be equal to one minus, one minus nine. Second point right over here, if we say this is kind of our, if we're starting at this And what's that going to be? Well, if we say that this Ourselves that slope, slope, is equal to, slope is equal to change The two points that we know? And we just have to remind We could just evaluate well what's the slope between To apply point-slope easily, we just have to figure out the slope. Were given two points that are solutions, that represent solutions to the linear equation. The slope of the line that represents the solution Satisfy the linear equation, and if you were to know Very easy to generate if you know a point on the line, or if you know a point that satisfies, where the X and Y coordinates So let's first thinkĪbout point-slope form. And I encourage you, like always, pause the video and see if you can do it. In both point-slope form and in slope-intercept form. Now what I want to do in this video is I want to say, well can weįind that linear equation and can we express it Represents all of the solutions to this linear equation. Now let's say we also know, we also know that when X is equal to six Y is equal to one. We have a linear equation and we know when X is equal to four that Y is equal to nine and we've plotted that I hope that this helped! I have never answered a question before, so I'm sorry if this answer seemed to go on forever. So you would set up the slope equation like so: So now you know that there is no y-intercept in this problem. To find slope you would do the following: Remember, it is change in Y over change in X because you need to find the independent variable for the slope. I bought 2 ornaments, so my points for the graph would be the following: Otherwise, you would be searching for Y, and you already know what it is. ![]() That is why you always do change in Y over change in X. ![]() So you already know what the dependent variable is. The dependent variable is the amount of money because it changes depending on the amount of ornaments. Every ornament I buy increases the amount of money I spend by $2. So say for example that I am looking for christmas tree ornaments. So when you are finding slope, you are trying to find the rate of change of the independent variable. It is not the change in X over the change in Y because X is always the independent variable in the situation, and Y is always the dependent variable in the situation. ![]()
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