Answer:
y=-x+2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-5-1)/(7-1)
m=-6/6
m=-1
y-y1=m(x-x1)
y-1=-1(x-1)
y-1=-x+1
y=-x+1+1
y=-x+2
Answer:
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: [tex]m=\frac{y1-y2}{x1-x2}[/tex]
Which means: m = [tex]\frac{-5-1}{7-1} = -1[/tex]
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
