Hello, we're going to look at horizontal and vertical lines. Horizontal lines are lines of the form Y equal some number, let's say 4. If we look at a line of Y equal 4, any point with Y equaling 4 will be on the line. So let's just choose two points at random. Here's the .14 and maybe -3 four. Any point with AY value of four will be on that horizontal line. So Y equals some number is the form of a horizontal line. Or it might be F of X equal 4. Remember that means that it doesn't matter what the X value is, that the Y outcome is always 4 or the range is always 4. Next let's look at the slope. The slope was the change of the YS over the change of the axis. So if we put the .14 in for the first location, remember up and down they have to come from the exact same .14 from the in the first location minus the point negative 3/4. We're going to end up with 0 / 4. And 0 / 4 is really just zero. So every horizontal line has a slope of 0. Now let's look at the vertical line. Vertical line once again, let's choose any points. Let's choose three, one, and three -3. Any point on on this vertical line is got to have X equal some value. In this case, X equal 3. There is no or F of X because by definition this is not a function. It does not pass the vertical line test. However, we do have a slope. If we look at our slope, we're going to do the change of YS over the change of X's. In this case we get 4 / 0. Once again, keep in mind that top and bottom had to come from one point, so that's my .31 top and bottom from the same .4 divided by zero 4 / 0. Oh, we can't divide by zero. This is actually undefined. Every vertical line has an undefined slope, So every vertical line has an undefined slope. That's really important. It's not that it doesn't have a slope, because it does. The slope is undefined, so every vertical line has a slope that is undefined. Be really careful. It's not that it doesn't have no slope, it's that the slope is undefined. There is a big difference mathematically. We're also going to look at intercepts Y intercept. We set X equal to 0 and solve for Y. So we get a point in the form 0B, the X intercept. We set Y equal to 0 and we solve for X. Or we get something in the form of a comma 0. Let's look at an example. If I had a line of the form 2X plus 3Y equal 12. Now remember it could have looked like 2X plus 3F of X equal 12 because that F of X is really just our Y. When we put zero in for X and solve for Y0 times, anything is 0. So we'd get 3 Y equaling 12 or Y equal 4. What that really means is when X was 0, Y is 4, and that's one of our intercepts. It's the .04. Remember, everything on a Cartesian coordinate plane should be given as a point. When we do our Y intercept, we're going to set the Y equal to 0, so we get 2X equaling 12 or X equaling 6. Once again, this is a point when X is 6, Y is 01234 or 5-6 if I connect those two points. I've now just graphed two X + 3 Y equal 12 by finding the Y intercept and the X intercept. Our last topic is standard line of a form. Standard line of a form is that the form AX plus BY equaling C The things that are important here, AB and C are all integers. That means no fractions, no decimals, they're all integers. Also, A&B are on the same side and a is positive. So let's look at an example. A is actually. It could also be 0 greater than or equal to 0. What's the case if it equals 0? If it equals 0, then we just have a horizontal line. So let's look at an example of this. Two X + 7 Y equal 8. Let's say we want to put that in slope intercept form. Slope intercept form says solve for Y. So we're going to subtract the 2X to the other side, and then we're going to divide by 7. So we got Y equal -2 sevenths X + 8 sevenths. So this ended in slope intercept form. It started in standard form. What if we had an equation that started in slope intercept form and we want to put it in standard? Well, we need to get all the X's and Y's on one side, so let's subtract that five six X + y equal 4. I also have to get rid of all the fractions and I need that first number to be positive. So if we multiplied the whole thing through by a -6, we'd get 5 X -6 Y equaling -24. So we've just gone from standard form to slope intercept form and slope intercept form back to standard form. Thank you and have a great day.