Please provide justification

y = -1 x + 2

Step-by-step explanation:

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

y = mx+b

m is the slope, and b is the y-intercept.

Now, to find m, simply substitue here:

Which means: m =

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 (1,1) and (7,-5).

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:

Either: (1,1). y=mx+b or 1=-1 × 1+b, or solving for b: b=1-(-1)(1). b=2.

Or: (7,-5). y=mx+b or -5=-1 × 7+b, or solving for b: b=-5-(-1)(7). b=2.

both gave us the same answer for b, which is 2.

Therefore, the equation of the line that passes through the points (1,1), and (7,-5) is:

Y = -x + 2