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(12 points, points each) U-mx+b of the line passing through the point (3, Witn Find the equation slope of 2...

Question

(12 points, points each) U-mx+b of the line passing through the point (3, Witn Find the equation slope of 2

(12 points, points each) U-mx+b of the line passing through the point (3, Witn Find the equation slope of 2



Answers

Find the slope of the line determined by each equation. $$3 x+2 y=12$$

In this problem. We have a few steps we must did find her final answer. The first thing is we're going to find two points that long maligned three times y plus two equals two x minus three. And once they find those two points were going to use the slope formula to find the slope of the lot Before we start fighting the two points, let's simplify our equation. Our equation says three times, while plus two equals two X minus three. I'm gonna use the distributive property to simplify the left side of this problem. So we're going to multiply three times why? And three times to to simplify three tons wise three. Why, three times two is six will equal to X minus three. Nothing on the rot side needed to be simplified, so it was left alone. Now that we've got the problem simplified, we're going to use our exit herself. And why in herself to find two points, we'll start with our X intercept. Our exit herself is where X will equal zero. So we're gonna rewrite the equation. And in place of eggs, we're gonna put zero, so we'll have three. Why? Plus six equals two times zero minus three. That will give me three y plus six equals. Two times zero will be zero, but it zero minus three will still just be negative. Three. So we're gonna mark that out. So that would leave me with negative three on the right side. We need to isolate my wife. Simple. Subtract six on both sides. So, three, Why will equal negative three minus six? It's negative. Nine divided by three. Why will equal negative three. So our first point on the line will be zero negative three. Our second point, We'll use the Y intercept. And this place, why will equal zero. So we'll rewrite the equation and put zero in place. And what? So now we're gonna have three tons. Zero plus six equals two X minus three. Three times zero will be zero and will still leave me with six on the left side. So we're gonna cross it out and have six equals two x minus three. I need to isolate my ex, so we're gonna add the three on both sides. Six plus three is nine equals two X, divided by two x will equal nine house. So my second point is going to be not have zero. Now that we have my two points, we're going to use the slope formula toe, find the slope of this line. The slope formula says our second Y coordinate minus my first y coordinate divided by my second X coordinate minus. My first sex coordinate will give you my slip so he'll will equal zero minus and negative three over non halves. Modest zero. Let's simplify the numerator where we have a monos. A negative. So LeBron change that to a plus zero plus three Ager nine house Modest zero zero plus three is three and non hams. Mona's zero is non Hafs. We need to simplify this more by dividing three divided by non house when you're dividing fractions were gonna make three as 3/1 and we're gonna divide it by the reciprocal of non hats, which means we're going to flip. So we're gonna multiply by two over. Not this will be a dividing problem, but multiplying by the reciprocal that is actually how we're going to divide three divided by nine house three times two is six, one times non is none and we can reduce six nights, other divisible by three So we could know bottom both by three. And they would give me too. Yes, so the slope of three times Y plus two equals two X minus three is to there's.

So we want to find the slope. Um, using these two points. So remember these two are these are X Y coordinates here, X comma. Why there ordered pairs come alive. And so our formula for slope is rise over one or change in why, that's the delta sign for change in over changing X. Or you can think why to minus y one divided by x two minus x one So, more specifically will level. This is like the first pair will subscript one. And then this is the second pair x to y two. So using that, that means that this negative three is my Y two and minus minus my wife I want which is negative one divided by and then my ex too. Is this to hear Too minus And then negative too. Is our xo one so minus, um negative. Two hopes. And it looks like we forgot that negative sign up there. So have negative three minus negative one. Which gives me, um, negative too. And negative. Aaron Positive to minus negative, too. That's the same as positive for so we can simplify this fraction further. That's negative. 1/2 a czar slope

For this problem, we're gonna be doing two sets of instructions that will correlate together for one final answer. The first thing we're gonna do is we're gonna find two points that lie on the line Y equals three X plus two That said, linear equation. Once we find the two points, we're gonna use the slope formula to find the slope of this line. So in order to find her points, we're gonna use the two intercepts we're gonna use the ex center Celt, and we're going to use the Y intercept now in the X, Enter Celt are eggs will always equal zero. So for this problem, we're going to rewrite the equation. But in place of X, we're gonna put zero. So now have Why equals three tons zero plus two, three times zero is zero and zero plus two is too. So my y coordinate is too. So this point is going to be zero soon. Our second point, we will use the y intercept. And just like the Exeter Celt Ah, they're very similar. But this time are why is going to equal zero? So we're gonna rewrite the equation with y equals zero. So zero equals three x plus to we'll subtract two from both sides. Toe, isolate the eggs. So cancel. So we have zero minus two is negative. Two equals three X. We're still trying to isolate the eggs. So we're going to divide my three on both sides, so X will equal negative 2/3. So the coordinates for the second point or negative 2/3 zero. So we're gonna use thes two points of zero to and negative too. Third's zero to find the slope of this line using the slope formula. The slope formula states that we're gonna eel more slope equals our second line coordinate minus my first y coordinate divided by my second X coordinate minus my 1st 6 coordinate. So for this problem, we're gonna have my second wife. Cornet is zero minus my first wife Coordinate is too divided by my second X coordinate is negative. 2/3 Modernists. My 1st 6 coordinate is zero. See, Romanos to is negative two and negative too. Third, Spahn, it zero is negative. 2/3. Now I'm pretty sure I can simplify this even further. So we're going to divide negative to buy negative 2/3 now if you have a calculator, you don't have to necessarily do this step, but I'm going to go ahead and show you how this one works. So the VOD by fraction, which is this bottom fraction we're gonna flip the fraction. So instead of negative 2/3 we're gonna have a negative three halves and we're gonna multiply so negative two times negative. Three is six and one times two is, too, which will reduce to three. So our slope for this line of Y equals three x plus two is three.

For this problem, we're gonna be doing two sets of instructions that will correlate together for one final answer. The first thing we're gonna do is we're gonna find two points that lie on the line Y equals three X plus two That said, linear equation. Once we find the two points, we're gonna use the slope formula to find the slope of this line. So in order to find her points, we're gonna use the two intercepts we're gonna use the ex center Celt, and we're going to use the Y intercept now in the X, Enter Celt are eggs will always equal zero. So for this problem, we're going to rewrite the equation. But in place of X, we're gonna put zero. So now have Why equals three tons zero plus two, three times zero is zero and zero plus two is too. So my y coordinate is too. So this point is going to be zero soon. Our second point, we will use the y intercept. And just like the Exeter Celt Ah, they're very similar. But this time are why is going to equal zero? So we're gonna rewrite the equation with y equals zero. So zero equals three x plus to we'll subtract two from both sides. Toe, isolate the eggs. So cancel. So we have zero minus two is negative. Two equals three X. We're still trying to isolate the eggs. So we're going to divide my three on both sides, so X will equal negative 2/3. So the coordinates for the second point or negative 2/3 zero. So we're gonna use thes two points of zero to and negative too. Third's zero to find the slope of this line using the slope formula. The slope formula states that we're gonna eel more slope equals our second line coordinate minus my first y coordinate divided by my second X coordinate minus my 1st 6 coordinate. So for this problem, we're gonna have my second wife. Cornet is zero minus my first wife Coordinate is too divided by my second X coordinate is negative. 2/3 Modernists. My 1st 6 coordinate is zero. See, Romanos to is negative two and negative too. Third, Spahn, it zero is negative. 2/3. Now I'm pretty sure I can simplify this even further. So we're going to divide negative to buy negative 2/3 now if you have a calculator, you don't have to necessarily do this step, but I'm going to go ahead and show you how this one works. So the VOD by fraction, which is this bottom fraction we're gonna flip the fraction. So instead of negative 2/3 we're gonna have a negative three halves and we're gonna multiply so negative two times negative. Three is six and one times two is, too, which will reduce to three. So our slope for this line of Y equals three x plus two is three.


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