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Good day students welcome to mathgotserved.com in this clip are going to be going over the solution to a fundamental to calculus test lets take a look at, one a says right that equation of the line L1 that goes through two four and three three so to write down the equation of the line given two points going to be using the point slope form of the equation of the line which is y minus Y one equals and X minus X one okay so in order to use this equation any three ingredients you need y one needs and any X one okay we have to points any of these two points, of I have is one one an excellent so let's Psalm is here X one y one so this is X one why one inning this is X to Y to so you can clearly see that we know of X one is roots write this in black X minus two in one one is four okay so you have the ingredients that we the left pieces we do not know what m is in order to find m were going to the simply uses the formula why two minus y one which is a rise over X to minus X one which is a rough we already have to work here is X one y one X to Y to which simply substitute these values into our so formula to find the slope of the line okay so you have three minus four why two minus y one divided by three minus to be minus four is negative one divided by three minus two is one so our slope is negative one I have everything we need to write a equation of our line so we substitute X one y one and in this equation will have all equation of L1 is why minus why one which is for equals the slope negative one times X minus two which is X one right this is the equation in points slope for if we desire to write this in slope intercept form basically multiply negative one to both sides in half four that yields y equals negative X minus minus one times minus two is for us to plus two plus minus two X plus two and then we at four to that okay so reduced that further will have why equals negative X plus six and this is the equation in slope intercept form for okay so the lower to answers for question number one the general form you have sufficient right let's take a look at question number two is as right equation of the line that goes through three negative one and is parallel two two X is three why equals for okay so you need is points and slope to write equation of the line very have a point here X one y one so we have X one is equal to three y one is equal to negative one we're going to be using the points to four of the equation of the line to generate our equation okay so the have X one y one Indian we need to find and we know that the slope of this line is premises outline so if you look at this line is in standard so you have this a line in standard form it to way to find the slope one way by taking the negative a over b so this is a set the answer is going to be negative to over three X one way orienting change this equation into all slope intercept form subtract two X from both sides and divide by three and you can see that the slope is four thirds eye negative two thirds so are to enter negative to over three so that's all information we need so equation of the line that one equation now what you want to note is that this is the call this out okay the outline below to other Linux kernel to L1 so let's go back to two so it L one is Carlo to two and that implies that the slope of one one is going to be equal to the slope of one two so the slope of this line is negative to purchase what the slope of the line going through this point and call to that line don't to is also going to be negative to third right and also okay is the side point is going to be difficult to this is normal to L1 and and why is going to be negative reciprocal of it to write to the one to keep these two points in mind the equation is going to be why minus why one why minus negative one is one equals negative to third X minus three okay so that equation in points of for right let's take a look at question of function into the X and these lines right here represents so it is where why equals the to the X is to so can express this as why equals the race to the X was to now what kind of translation is this you have plus two X to the X everything we need you going to be shifting of two units to the left okay so you see the center right here in the shifted two units to the left in order to generate this transformed function okay so let's go ahead and take a look at what it looks like right so there goes your resulting graph is is you notice this point right here the shifted two units to the right and then you have this line right here retain will be our results into at zero and for that pattern the same as this is shifted two units to the right okay so this is the graph of this function right s

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