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Parameterize the line from (4, 1) to (6, ~2) so that the line is at (4, 1) at t 0,and at (6, 2) att = 1.,0 € (t) =-4 + 2t y (t) = -1 - 3t0 = (t) = 4+ 2t y(t) ...

Question

Parameterize the line from (4, 1) to (6, ~2) so that the line is at (4, 1) at t 0,and at (6, 2) att = 1.,0 € (t) =-4 + 2t y (t) = -1 - 3t0 = (t) = 4+ 2t y(t) = -1 -3t0 = (t) =4 -2t y (t) = 1 + 3t0 * (t) = 4 +2t y (t) =1 - 3t

Parameterize the line from (4, 1) to (6, ~2) so that the line is at (4, 1) at t 0,and at (6, 2) att = 1., 0 € (t) =-4 + 2t y (t) = -1 - 3t 0 = (t) = 4+ 2t y(t) = -1 -3t 0 = (t) =4 -2t y (t) = 1 + 3t 0 * (t) = 4 +2t y (t) =1 - 3t



Answers

Parameterize the line from (4,1) to (6,-2) so that the line is at (4,1) at $t=0,$ and at (6,-2) at $t=1$

In the question We're even the permit questions when we have the X in Cochin of formalist three d Why could humanist God bless six day here to find the X y questions From the first question we can absolutely t to get the ICO June uh, four minus acting even amid three. And when you just stay here to Buddha Majesty and from again and why we could humanist you plus six times that you know you could you my formalist x over three It was indifferent gonna months Jew six divining with three good juju So plus eight months to acts. Therefore, we're gonna minus two x six. So it doesn't mean standards slop You go to the months to so we can scan the graph now. So we have the Islamic culture Minister and the UAE into Semeka to six. So this one and then smiles, Joe. So we're going down. Just one. Um So this will be the act. Why six and is only with three

It wasn't well, given that permits were given the from the question off that I so even, uh, because you don't want to three. Then, Gus, the Tim's phones. There are 16 and then we can tension into the permit equation. I'm the form actually going to one. So we want to use the first time here, So it will be Thanks Echo to one blessed 40. And for the why, when you the second term. So why we could you know that you blast is 30 and follows. They would get the last one. B Z equals unit three minus 60. And this will be the equation. Barometric question on the line.

For this problem. We are asked to show that R. One and R. Two to find the same line where R one equals three negative 14 plus t times 8 12 negative six. And R two equals 11. 11 negative two plus two times 46 negative three were given a hint to show that our two passes through three negative 14. And that the direction vectors for R. one and R. two are parallel. So let's start with what the hint first indicates. Now let's see here. So You can see that if we want to pass through the .3 we need to take a negative value for T. Now 11 -4 is not going to equal three. In fact that will equal seven But 7 -4. Well give us three. So um or rather not seven yeah seven miles four. So if we take our starting point and subtract off to t. Then we'll get actually I'll write this out explicitly. We'd have that are two of negative two Would be 11. 11 negative too minus To. Actually I'll write this out explicitly. Plus negative eight negative 12 positive six. Which is then going to be the .3 -14. So we can see that we do pass through that point then to show that the direction vectors are parallel. Well the direction vector for our one which I'll say um just D. i. r. of R. one eight, 12 negative six. But we can reduce that If we divide by two we don't change the direction but we get 46 -3. And we can see that that equals the direction vector are too So since we can change the, since we have the direction vectors are the same or are parallel, and we do pass through the same points. That shows that yes, they are the same line.

Okay, So we're supposed to promise to rise a line that goes from the point point four comma One at T equals zero to the 0.6. Common negative too. At T equals one. Come. Huh? Going to begin by making a table T x? Why? T is zero and then one at T equals zero X is for And why is one at T equals one X is six And why is negative too? So if I look just at T vs X, that is not what I wanted to D'oh! If I look just at t vs Ex e Don't think I have a highlighter here, let me try square. Oh, that didn't work either. Well, nevertheless, I'm gonna look at T Vs Ex so the X values are for and six. So the slope is x two minus x one over t to minus t one. That looks a little strange because we're used to ex being in the denominator. But in this case, acts is a function of tea. The second X is six. The first X is for the second. T is one the first T zero six minus forest to one minus zero is 12 divided by one is too, and the Y intercept is. Although in this case it's the X intercept where t ah is zero is for All right. So we'll do the ah, this one's for Why? Why? To minus y one over t to minus t won the second. Why is negative too? The first? Why is one and ah the second t minus the first tee Negative too minus one is negative. Three divided by one is still negative three and B is one because t zero we just pick out the point. The number where t zero So are two equations are x he quarrels two x no tea t plus four and why equals negative three two plus one MX plus B. Just write that up here. We're using M X plus B, but T is going in the place of X and either X or why are going in the place of why


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