Answer:
8
Explanation:
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (3,5), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=3 and y1=5.
Also, let's call the second point you gave, (2,6), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=2 and y2=6.
Now, just plug the numbers into the formula for m above, like this:
m=
6 - 5
2 - 3
or...
m=
1
-1
or...
m=-1
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=-1x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(3,5). When x of the line is 3, y of the line must be 5.
(2,6). When x of the line is 2, y of the line must be 6.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=-1x+b. b is what we want, the -1 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 (3,5) and (2,6).
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:
(3,5). y=mx+b or 5=-1 × 3+b, or solving for b: b=5-(-1)(3). b=8.
(2,6). y=mx+b or 6=-1 × 2+b, or solving for b: b=6-(-1)(2). b=8.
See! In both cases we got the same value for b. And this completes our problem.
The equation of the line that passes through the points
(3,5) and (2,6)
is
y=-1x+8