Question
At approximately which integer value of x does the graph in Figure 2.1 have each of the following slopes?Figure 2.1a) -2b) -1c) 1d) 2
At approximately which integer value of x does the graph in Figure 2.1 have each of the following slopes? Figure 2.1 a) -2 b) -1 c) 1 d) 2
Answers
Find the equation of the line whose graph is shown in Figure $21 .$ a. $y=-\frac{1}{2} x-1$ b. $y=-2 x-1$ c. $y=\frac{1}{2} x-1$ d. $y=-2 x-2$
Hello. Listen, we have given a cushion here. Question is, why's it will do more off X minus one place to and two points are given. One point is one and 2nd 1 is he points two and four point What we need to do here just for this point in this given equation And if it is satisfied than this point is in the rough. So first putting this point, there is one in the draft. Why's it gonna do X minus? One more plus two. So But we will get one is they want to. This one becomes my best one restroom. There is a door three which is not equal. One is the article that is Elytis is a Nordic Will do so simply can't stay. This point is not in the Now you taking second point second point days, one to four point in the equation. I think we should knees x minus no more. When we used this point for this 14 point on using this 3.2 minus one less we'll get here for so simply begin here. Right this point. He's in the thank you
Okay, so this one says, if the two lines interested at point a B, what is the value of a plus B? Well, so let's go in and try to fill in the information that we know. We know that one of the lines have a slope of two and goes to the point. Welcome. Eight. Well, we know that our equations you're all in with the form of y equals MX plus b r m is our smoke and B is our by Anderson. So if it already tells us that our slope is too, you know, it's why is equal to two x plus B and we just have to find that intercept value. So from there, Reznik in order to find out what this pluck in this point. But it goes through as the X come alive two times. One plus B is equal to eight. Now we know that Khun subtract two from both sides. Giving us that six is equal to be so. In order to complete this equation, we know that it's just going to be six to expose six. So that's our first equation on that. We know that the second equation goes through one color one and two come one to them again. We still have to find our vehicles and most sports peace. I'm going to start out by finding this slope. No defender Slipper doesn't do y two months. Why one over X to minus X one. That's gonna be one minus two over to minus one, which gives us negative for one. So from there, I know it's going to be wise Eagle to negative X plus B. And again, we could just put in any of those points. So I'm going to go out and plug in that first point one comma two, at which point we got to a sickle to negative one plus B. So then, if we add one to both sides, we get that b is equal to three. So our second equation is going to be Y is equal to negative X plus three. So here's our first equation, and here's her seven equation. So then we know that they interested at this point so foot intersex than we have to find thie ex coming. Why, after we've come combined the two equations. So here's our second equation. So I'm going to just go and use substitution to set these two equations equal to each other because this's ableto and that's what's why. So I was going to happen equal to each other. To have two X plus six is he wants necklace expose three. I'm gonna add extra both sides giving me three acts and then I'm gonna subtract six from Besides giving me negative three So x is equal to negative one because I divided both heads back to me. But again, if we're looking for a plus B, we also need the bee value, which is our Why about you? So I'm going to put this back into any overy equations and who's going to plug it into this one, and I'm gonna get that y is equal to negative of negative one plus three negative negative cancels out. That gives me four. So here now we have our why value and our X value. So our guess values right here or y values right here. If we add them together, we got three. So B is our answer
And this problem we're going to we're going to reflect the's points across the x y y equals X axis. So I have Michael's X, which is this letter here. So more points are gonna be negative to To which is a negative one three is be one to which is C and the which is negative to negative two. So our new points are going to be see right here. Be to be right here. Hey, we'll be right here and D actually stays where it is because it's already on this line.
Were given four functions and we want to match them the four graphs in figure 21. So let's start with a function a. So function A is one over x squared minus one. zero. It is -1 and we can see that it's a Santos to zero as X gets large, both positive and negative. So um and it it also has a vertical ascent tote Um, x equals plus or -1 because the denominator is zero at those points. And if we look through our plots, we see that that corresponds to uh two D. The next function is we have x squared divided by x squared plus one. This function has to be zero when x equals zero. And as X gets very very large, this thing gets neglected. And so this becomes one. So why approaches one? As X gets very very large, both positive and negative. And that means that we have graph a next function Y equals one over X squared plus one At Zio. It's one. And as why why goes to zero again as X approaches plus or minus infinity? Because this denominator gets very very large. There are no acid tablets because this is *** never zero. As long as X is a real number anyway. And so that means that we have graph B. And finally, for the last one we have X over X squared minus one When X0, Y zero. When Y equals why goes to zero as well as X gets very very large. We wind up with a he won over X. Um Pratt type function. And so that goes to zero. We also know that we have a santos at plus or minus one, but we can clearly see that that's obviously the only one left is C.