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A student was asked to find the slope of the line through the points $(2,5)$ and $(-1,3) .$ His answer, $- rac{2}{3},$ was incorrect. He showed his work as$$ rac{3-...

Question

A student was asked to find the slope of the line through the points $(2,5)$ and $(-1,3) .$ His answer, $- rac{2}{3},$ was incorrect. He showed his work as$$ rac{3-5}{2-(-1)}= rac{-2}{3}=- rac{2}{3}$$Give the correct slope.

A student was asked to find the slope of the line through the points $(2,5)$ and $(-1,3) .$ His answer, $-\frac{2}{3},$ was incorrect. He showed his work as $$\frac{3-5}{2-(-1)}=\frac{-2}{3}=-\frac{2}{3}$$ Give the correct slope.



Answers

A student was asked to find the slope of the line through the points $(2,5)$ and $(-1,3) .$ His answer, $-\frac{2}{3},$ was incorrect. He showed his work as $$\frac{3-5}{2-(-1)}=\frac{-2}{3}=-\frac{2}{3}$$ Give the correct slope.

Okay, so we're asked defying the slope, given these two points? Yes. So because our slope that secret beautiful one. Okay, so let's label falling as x one and white one. And this as x two comma y two. Okay, so it's begin what we have. So we have. Why? To its three minutes. Why one which is on Native Force. That's close for over X two. That's one minus, uh, X one, which is five. Okay, so that use me seven over negative four or are slope

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

To find us that we need use off slope. Former. So this is gonna be your X one in this. Your ex too. Does your wife want? And your y two now Still from this? Why? To minus Why? One over X two, minus X one. Now all you do you do is pregnant. So white to is three. It's attract five and then extrude negative one and then subtract two. Now you just simplify it. Three minus five s name too negative. One month is too is negative. Three because of negative with a negative is a positive. It's gonna be a positive to over three extra slope.

To find this looking gonna do. Negative for minus two all over one, minus negative. Three. When you simplify, you can negative 6/4. So be negative. Three or two. But the student got positive. 3/2. So that means the student did not align the Why the second point with the first point? Because you have to dio why? To minus y one x two minus X.


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