Okay, so we're writing equations of lines today. This whole section is going to be rooted in slope, intercept form. So y equals MX plus B. So if they're giving us both a function of slope, then here are the things that we know, we know an X. And we know why do I also know slope that would be our M. So the part that we're missing that is crucial is B. So what we're gonna start with is that y plus B equation, we're gonna fill in and the X and the y so Y is e from our coordinate, and it's 3/2 that was our.

Solute X is 4, and then we don't know yet. So right here, we're going to multiply this, if you have a heck of a time with those fractions multiplying by entire numbers, you can throw that into a calculator. You could also multiply these two numbers. So 3 times 4 is 12 and then divide by 2. We should make 6 all right. So right now we're 8 equals 6 plus B. So we solved this like a little baby, one-step equation, we'll subtract 6 from both sides, leaving me with 2 for B.

Now remember B is not your final answer. We. Are trying to write the equation of a line, and that should be formatted like y equals MX, plus B.

So I'm gonna fill in the M from the equation, keep the X. And then that should be your final answer and that's also how you would like to type that into delta mac. Now there are some special cases as well. Same idea. This is where you're still going to have an X a Y and an M, but note that our M is 0. So you can still treat this like y equals MX, plus B and do it the same way that we did up above filling in. Negative 7, filling in 0 5 and not going be still 0 times 5 is 0, which just leaves us with negative 7 for B, which is I fill that in I get this weird equation that looks like y equals 0 X, minus 7, but remember 0x is nothing.

So we get something like this. If you think back to what we did in class, this guy, right here is actually a horizontal line. And you can know that directly from having a slope of 0. So if you remember that this guy is a horizontal line, you can know that it's equation is going to. Start with y equals, and then you can just grab this Y value from right here and throw it into your final equation. If you want it the fast way now on our other special case, okay, that's where we have an undefined slope, okay, still M, but I can't, throw a word into an equation.

So on this one, you have no choice, but to know that undefined does mean a vertical line and vertical lines are gonna start with x equals, so I just want to grab that x value for my coordinate and that's.