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The straight line $y=x-2$ rotates about a point where it cuts the $x$-axis and becomes perpendicular to the straight line $a x+b y+c=0 .$ Then, its equation is(A) $...

Question

The straight line $y=x-2$ rotates about a point where it cuts the $x$-axis and becomes perpendicular to the straight line $a x+b y+c=0 .$ Then, its equation is(A) $a x+b y+2 a=0$(B) $a x-b y-2 a=0$(C) $b y+a y-2 b=0$(D) $a y-b x+2 b=0$

The straight line $y=x-2$ rotates about a point where it cuts the $x$-axis and becomes perpendicular to the straight line $a x+b y+c=0 .$ Then, its equation is (A) $a x+b y+2 a=0$ (B) $a x-b y-2 a=0$ (C) $b y+a y-2 b=0$ (D) $a y-b x+2 b=0$



Answers

A line has the equation $y=3 x+2$
\begin{equation}
\begin{array}{l}{\text { (a) This line has slope ______. }} \\ {\text { (b) Any line parallel to this line has slope ______. }} \\ {\text { (c) Any line perpendicular to this line has slope _____. }}\end{array}
\end{equation}

Number 44. It asked us for the slope of a line that is perpendicular to a X plus B Why cost see equals zero. So the first thing when you do is we need to find out what this slope is of this line right here. And to find the soap of that line, we need to do get into slope intercept form, which means we need to get why by itself. So we're gonna subtract, see? So a X plus b why equals negative c When I subtract a X over that's gonna give me be why equals negative a X minus C and divide by B So the slope of this line, it's negative a over b. So if we want a lot is perpendicular, we have to take that negative a over B and we have to find the opposite reciprocal. Well, Officer, reciprocal means we're gonna change the signs. That was negative. So now it's going to be positive. You were going to flip the fraction the baby was on the bottom. He's now gonna be on top. Hey, was on top. It's not gonna be on the bottom. So my slope of a line that is perpendicular to expose B y plus C is be over a

Problems were given to the equation expose to iPods 30 and were asked to find when experts to I was three is perpendicular to the graph of a expose. Three wipers to was here basically find the value of a basically fine about the way that makes these two lines perpendicular. So what we're gonna do is we're gonna write each form And why was MX plus P terms? So starting on the right nor detritus and like was that might be term. We're going to subtract the minus to lie on both sides and you get minus two wise. He would expose three, divide out by minus two, and you're left with the MX was Speed former here and then on the right sad turn into the same thing. We're gonna subtract by Linus three while on both sides. And that's gonna give you a X plus two on the other side. The Honduran divide. I'd like minus three. So here to get minus 1/3 x minus 2/3 this slope of off this graph want this this'll line right here is why he calls the slope is negative 1/2. So the slope that's perpendicular to this is going to be positive, too. Because positive too. Yeah, because, ah, it's going to be the negative, reciprocal off, whatever it is. So it's gonna be part. It's gonna be positive to the negative past it too, then. So, uh, we're gonna want this positive to be equivalent to our minds a over three. And solving this out because that are a value has to be, uh, minus six. And indeed, it's a choice. That course ones who with minus six is insane choice, eh?

So we given Equation. Why's he go to three X Plus two? And so for a were asked to figure out the slope. And so we remember that our equation of the line is why is able to, um X plus B, where m is a slope. So we know, Got this line has a slope of Serie so for being were asked to forget the soap of anyone parallels to remember any line parallel. How's the same slope? So you know that any line parallel also has a slope of Serie. Now we know that for any line perpendicular, it is a negative reciprocal. That means they will have a slope of negative wondered.

Okay, So first, when you determine the X intercepts were exit dress up when it's set, when why is equal to zero? So we have to acts. Is a go to for each wax plus three time Gerald minus 12 is equal to zero getting us two x equals 12 accessing into six. So another ex interest out there's 60 Next, we are asked to find the y intercept. So we're going to the UAE interceptors one X equal to zero. So we have two times zero is equal to three times zero plus three. Why is equal to 12? It gives three wise eagle 12 which gets us wise able to four. Do not are why intercept is 40 or sorry, zero for all right. Next we're asked to write Justin someone just for so when you actually are. Why? So we have two X plus three y is equal to 1912. We bring the white over for weeks. Bring the X over to leave. Why over there? Actually, this should be minus 12 is equal to zero. We leave the why would bring over 22 x and 12 to get us three. Why, tho X plus 12 which gets us wise. It was nearly 2/3 X plus four. Okay, so now the last thing that we have left is to figure out herself. And so remember, it is why is equal to one X plus B where a mazar slope So we know they're slope in this case is negative tooth hurts.


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