##### find the equation for the line through the points (7,2) and (-2,-4)

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the line through (7,2) and (-2,-4)

Thank you for the opportunity to help you with your question!

You want to find the equation for a line that passes through the two points:(7,2) and (-2,-4).

First of all, remember what the equation of a line is:

y = mx+bWhere:- m is the slope, and
- b is the y-intercept

First, let's find what **m** is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.Now, what about b, the y-intercept?To find b, think about what your (x,y) points mean:For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (7,2), point #1, so the x and y numbers given will be called x_{1}and y_{1}. Or, x_{1}=7 and y_{1}=2.Also, let's call the second point you gave, (-2,-4), point #2, so the x and y numbers here will be called x

_{2}and y_{2}. Or, x_{2}=-2 and y_{2}=-4.Now, just plug the numbers into the formula for

mabove, like this:

m=

-4 - 2

-2 - 7or...

m=

-6

-9or...

m= ^{2}/_{3}So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y= ^{2}/_{3}x+b

- (7,2). When x of the line is 7, y of the line
*must be*2. - (-2,-4). When x of the line is -2, y of the line
*must be*-4.

Now, look at our line's equation so far: **y= ^{2}/_{3}x+b**.

**b**is what we want, the

^{2}/

_{3}is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (7,2) and (-2,-4).

So, why not plug in for x and y from one of our
(x,y) points that we know the line passes through? This will allow us
to solve for b *for the particular line that passes through the two points you gave!*.

You can use either (x,y) point you want..the answer will be the same:

- (7,2). y=mx+b or 2=
^{2}/_{3}× 7+b, or solving for b: b=2-(^{2}/_{3})(7). b=^{-8}/_{3}. - (-2,-4). y=mx+b or -4=
^{2}/_{3}× -2+b, or solving for b: b=-4-(^{2}/_{3})(-2). b=^{-8}/_{3}.

(7,2) and (-2,-4)

is

y=^{2}/_{3}x^{-8}/_{3}

Please let me know if you need any clarification. I'm always happy to answer your questions.

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