A Student Asked me to Find the Distance

so a student sent me this question online and I actually went to my live stream and started exploring it but the problem was guess what I graphed it wrong so everything I did on that live stream was completely incorrect because I don't know on the live stream I just had a mental fart in my brain and I was like man I got to go ahead and correct this I got to go ahead and fix the mistake and show you what I should have if I had a little of time and I wasn't on a live stream how I should have approached the problem so as I already previously showed we have a an equation of a line Y = 1 6X what was it plus 6 and we want to be able to determine does this point how far is the point from the line so I went to go and graph it but actually I did a slope of six over one instead of one over six that was my mistake guys it happens even to somebody that's done thousands of math problems you're capable of doing those things and just like when you take a test sometimes when I have a live stream like I'm not thinking clearly right there's people that are watching everything that I do and it messes with my brain so I get it when you take a test and you have this anxiety and it's like all the stressors breathe slow down and let's go ahead and think about this the first thing I always want to be able to do especially on an equation like this which I should have done first is well let's just go and double check to make sure that this point does not lie on the line because to do the work to be identify the distance from this point to the line is a little bit of work and so what I should have done first is say well this is an X and a y coordinate can I plug this point into this equation and if that makes it true then that means that point lies on the line so I replaced a y with five and my x with A6 I don't know why I put the one over six in parentheses I didn't really need to do that but it it is what it is so 1 over 6 * -6 is just going to be a negative 1 so in this problem guess what guys the distance from that point to your equation is zero look how quickly I was able to do that that's what I should have just gave the student the answer on and it would have been real quick it would have been real fast but I didn't even think about that on my live stream now the student might have still been confused oh so anyway the distance is going to be zero since it lies on the line but Al sometimes students they might have been asked this question and maybe they chose the wrong one because they wanted me to actually go through the process of how do you find the distance from a line to a point well there's actually a formula for that and a process so how about we change up the problem real quick so for those of you that are curious on how to do a problem like this why don't we just change up the numbers to the point a little bit and so therefore we can identify what that did distance is going to be now the important thing is when we are doing when we're trying to identify the distance from a an equation to a point we don't want to use our slope intercept form which we're going to want to use is going to be using a standard form of the r line so therefore what I simply need to do in this case is I need to go ahead and get all these values over to the same side to identify my a b m my C now it's very important that you notice that these are capital letters and what that means is we want these to be integers not fractions so therefore to get this one over six to not be a six anymore I'm going to need to multiply everything times a positive 6 now I'll have a final equation of a 6 Yus a xus a 36 is equal to a zero so therefore if we just go ahead and label this my a is going to be a negative 1 my b is going to equal a POS 6 and my C is equal to a - 36 now the next piece of information is I need to identify these points but we're not going to use X and Y what we're going to use for this formula is just p and Q so p is equal to a -6 and Q is equal to a pos4 so now once I've identified my abc from the standard form make sure it's in that form right don't use this you got to use that and I've identified my PQ which is the point that I want to find the distance from now all we're simply going to do is plug it into the formula which I do not memorized but I will write out for you H see told you didn't have a memorized okay so now all we're going to do is just plug chug and simplify I'm run out of a little space so I'll try to do my best so we have a which is -1 * P which is a -6 now again notice this is an absolute value so I am going to be using parenthesis for everything I plug in that's going to be plus a b which is going to be a 6 * my Q which is 4 plus a c which in this case is going to be a -36 and the absolute value and then I have the square root of an a squ which is a -1 qu^ 2 plus a b^2 qu^ s which is going to be a 6 squ okay so let's go ahead and write out the values up top just because I'm running out of a little bit of space I can find the right there we go- 1 * 6 is going to be a POS 6 6 * 4 is going to be a 20 24 and therefore a - 36 is just going to be a 36 so if I go ahead and combine all of those up well 6 + 24 is going to be a 30 30 minus 36 is going to be -6 but remember ladies and gentlemen it's absolute value so distance equals absolute value of a -6 is going to be a positive 6 and then over here I have a - 1 s which is 1 a 6 s which is 36 36 + 1 is going to be a 37 but that's under the radical so therefore my final answer is a 6 over the squ root of a 37 hope that helps