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

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the line through (7,2) and (2,4)
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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 yintercept
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 yintercept?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 m above, 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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