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To graph the equation $y-4=- rac{2}{3}(x-2),$ we start at the point _____ and count _____ units to the right and _____ units down to locate a second point on the li...

Question

To graph the equation $y-4=- rac{2}{3}(x-2),$ we start at the point _____ and count _____ units to the right and _____ units down to locate a second point on the line. The graph is the line joining the two points.

To graph the equation $y-4=-\frac{2}{3}(x-2),$ we start at the point _____ and count _____ units to the right and _____ units down to locate a second point on the line. The graph is the line joining the two points.



Answers

Graph each equation.
$$
4(x-2)=(y+3)^{2}
$$

Have a graph of the equation four times the quantity X minus three squared minus two. You should get a graph looking something like this, a very thin proble that barely enters the fourth quadrant and hits the Y axis at zero.

We have been asked to graft this problem showing in this equation. My minus two squared includes four times the sum of X plus three. First thing you want to do is identify that single variable and get it by itself first, so we're going to have to divide both sides by 1/4 1st you're well defined both sides by four first to get went forth times. Why minus two squared equals the sum of exposed Tree X is still not quite by itself. So we're going to subtract three from both sides to probably get the creation 14 times why Minister Squared minus three equals X. Just going to rearrange this a little bit. So it's a little bit more comfortable to work with. X equals 1/4 times. Why minus two squared minus three. Notice that this isn't the same format as X equals a times why, plus Kay's squared plus H and using this the for Tex. It's located at each comma Negative K, which means for us, the Vertex is going to be located at our angels. Negative three Negative three. Nora for Texas going to be located at positive to negative negative to positive, too. That will help us a little bit to get this set up. Me? Why access? Trying to think. I think it opens to the side. It's going to open to the right. So what we learned from this is that the first Texas located at negative 32 it's a negative 3 to 12312 right here. And I know that it's gonna open up to the rate. So let's go ahead and find her focus and direct tricks. Pixels are always useful. First thing we need to know is what is C? So we're going to use a to find C Hey, e equals one over four C and r equals went for him. This means that Seamus equal one. What does that tell us? Well, that tells us that to the right of our for text, just one unit is our focus. Uh, see, negative to two. And our direct tricks is the vertical line. X equals negative for so we know the problem is going to go through the Vertex and open up to the right. Now it's always hard to grasp a proble just sketching it. So we need to put in some points to find out what inputs and outputs we have, since this is a function where why is the input or table is going to look a little funny? We're gonna start with wife first and find out what we get for X. For example, I'm going to pick 00 is always an easy number to work with. We'll put zero in if I put zero in for why I get zero minus two. Just negative, too negative. Two Squared is four four times one for it's one one. Minus three is negative, too. This is the point negative to zero. No problems are symmetrical with their line of symmetry. Line of symmetry goes to the focus and vortex, which means there's another point exactly across from there. We know the problem goes through these three points. It's always a good idea to get one more point on there so you can get a more accurate graph. So let's pick another value for why. See, I'm trying to think of something that will end up nice. What's divisible by four. After it's squared, try oh his treat four. Okay, here we go. Four minus two is two to square. It is four. Oh, wait. You already did that one Your sport. 1234 It's also negative too. All right, let's try eat. Do I have enough? Speaks for eat 6 to 8? Yeah, this will be true for negative, Uh, suddenly gonna beat, but you get a six. All right, Plunkett, You gonna beat it? Mean positive? Aiden ain't minus two is six six squared is 36 36 divided by four is nine and nine minus three and six. So that tells me when Y equals eight. X equals six two. Thanks. Where? This point right here. Why? So just noticed the tables backwards. So it might take you a minute to orient yourself. But my equal date an X equal six again. It's symmetrical across the Linus symmetry right here through the focus in the protects. So let's see. Three Were I six right there. And then you can connect those points to make fairly accurate problem Who hold it

So if his equation point slope form on that equation is why minus four equals three times exposed to. So the easiest thing to identify it out of this, probably is that the slope of the line is three or three over one. Um, talk about that in a second. The other part is the point that it runs through. That's why it's called Point Slope is gonna be the opposite of that in the opposite of that. So it runs through the point negative to positive for negative to positive for. Okay, so that's what we do. First, I'm gonna go over to my, um, Cornet playing here. I'm going to go to Negative to positive four and on a plot of point rate there, Um, I slow fists. Three. That means I should go up three and write one. But I kind of don't have that ability because my grass not big enough, so I'll go down three to go down three and left one. That's the same as going up three and right one. And that gives me another point. I think so, that I make a nice straight line because I don't have the ability to use a ruler on this format. I think I'll do another point. So good. Down another 1 to 3 over another one down 123 left another one down, 1 to 3 over another one. And now I should be able to make a nice straight line that represents this equation. So it's got a slope of three up, three over one up, three over one up, three over one, and it runs through the point negative to four. So this is a first for me. So let's try this. You should definitely use a straight edge. And if you don't have access to a straight edge repeated slope down three over one down, three, everyone is probably your best bet. There's the line of this equation represents.

Were graphing lines by making tables of values or graphing equations. This one is gonna be a line. But, um, so I'm gonna do multiples of four because I'm looking at, um, you know, I'm gonna have to divide by force. It is. The way I look at this is 1/4 of negative. Eight is negative. Two times three is negative. Six plus four is our plus. Two is negative for so negative. Eight. Negative. +1234 Do that again. 1/4 of negative for his negative one negative one temps. Three is negative. Three plus the two is negative. One said Negative. Four negative. One 3400 close to is to that's an easy one. Ah, three force of four is three plus two is five. It's 123412345 and 3/4 of a dis six and six plus two is 888 There's eight. There's eight right there. And if we draw a line through, all those points will have the line. That represents all the solutions to that equation.


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