Answer:
C. y-1=2(x+2)
Explanation:
A. y-7=2(x-6)-point slope form: y-y1=2(x-x1)-coordinate point: (x1,y1)=(6,7)
Now let's check that the other point works-just sub in the coordinates for the x and y variables.
y-7=2(x-6)\\-1-7=2(2-6)\\-8=2(-4)\\-8=-8
So answer choice A. goes through both points, so no.
B. y=2x-5-slope-intercept form, so just sub in both sets of coordinates separately to see if they each work.
y=2x-5\\7=2(6)-5\\7=12-5\\7=7\\equal
y=2x-5\\-1=2(2)-5\\-1=4-5\\-1=-1\\equal
Both work, so no.
C. y-1=2(x+2)-point slope form that gives us first coordinate set--(-2,1)
Except that the point is actually (2,-1) not (-2,1). That means that answer choice C is not an equation of the line thaat goes through (6,7) and (2,-1), so yes.
D. Anyway, if we check D--y+1=2(x-2)--coordinate point given: (2,-1), which is correct, so no.