Hello wonderful mathematics people. This is Anna Cox from Kellogg Community College. Slope intercept form of a line is Y equal MX plus B&Y equal MX plus B. The M is our slope, and slope is the rise over the run, or the difference of the YS over the difference of the X. Sometimes we think of it as Y 2 -, y one over X2 minus X1. Or equivalently we could say Y 1 -, y two over X 1 -, X two. The important part of that is that up and down is from the same point, so as long as they're from the same point location wise in the problem, we're OK. So this X2Y2 represents a point, X1Y1 represents a point. So as long as either the first point comes first or the second point comes first, both times those are equivalents. Now the B is our Y intercept, or where we intercept the Y axis and it's the 0, BY intercepts are really, really, really always points. Remember that that's important. Zero B. So when we look at this example, Y equal 3/4 X. The number that's multiplied with the X is always our slope. So in this case 3/4. So it means we're going to go up three and to the right four because they're both positive numbers. the Y intercept is the number that's not being multiplied by the X. So in this case it's the .02. So on the graph, we're going to go up two on our Y axis, hence the Y intercept, and then we're going to go up three from there and to the right 4 we're going to go up three and to the right four again. The more points, just the more accurate our line graph would be. Up 3 and over 4 could also be thought of as down 3 and left 4 because a negative divided by a negative is still a positive. So instead of going up three and right four, I could go down 3 and left 4. Connect those points. Now, if we wanted to, we could actually choose one of these points to see if it was really on the line. Let's see, this is the .4 and 5 S Remember 4-5 a point how far over we went on the X and how far up we went on the Y. If it's on this line, I should be able to put the Y in and the XN and come up with a true statement. Well 3/4 * 4 is 3, so does 5 equal 3 + 2? And the answer is yes. So that's just a check that I could choose a pointer 2 to make sure I graphed it correctly. I'm going to let you try one of these. Now the important, another important piece is that slope intercept has to be Y equal with a single Y by itself, an understood one Y. So if we're given 2 points and we want to find the slope, literally, we're just going to take and we're going to subtract the YS over the subtraction of the X's. So 2 - 0 is two, 1 - 4 is -3 We don't typically leave the negative in the bottom, so I'm just going to move it up to the top -2 / 3. Or you could write it with the negative out in front. Now the negative out in front is a little harder for slope because the slope is telling us direction and distance. Now remember I said we could have the other point come first. So 0 -, 2 / 4 -, 1 zero -2 is -2 four minus one is 3. Look, we get the same answer. It doesn't matter which point came first as long as that 04 was from a single point or this 21 was from a single point. So you're going to try a couple of these. Our highlights to remember, 1 * X is really just X. So the slope here is one. If the slope is one, remember that one could be really thought of as 1 / 1, or any whole number, say 5 could be thought of as 5 / 1. So we'd go up five and to the right one negative a / b equal negative a / b or which also equals a / -b. So in this first case, we're going to go down and to the right. In the second case, we would go up and to the left. And then another one to just remember is a / b is the same thing as negative a / -b. So this one we're going up and to the right, but that's the same thing as going down and to the left. A / B is a what we call a positive slope. So the positive slope is going to start in the lower left somewhere and go up to the upper right over here. This other one is what we call a negative slope, and it's going to start in the upper left and go down to the lower right. So this is a negative slope and this one's a positive slope. Thank you and have a wonderful day.