The first option is the point-slope form for the given point.
Step-by-step explanation:
Step 1:
As we need to calculate the slope, m and coordinate we use the point-slope form to find m and the coordinate.
The point-slope form is [tex]\left(y-y_{1}\right)=m\left(x-x_{1}\right)[/tex],
the given equation is [tex]y-15=-2(x+1)[/tex].
Step 2:
By comparing both the equations, we determine the values of [tex]x_{1}, y_{1}[/tex] and m.
[tex]\left(y-y_{1}\right)= (y-15)[/tex], so the y coordinate is 15.
[tex]\left(x-x_{1}\right) = (x+1)[/tex], the x coordinate is; [tex]-x_{1} =1, x_{1} = -1[/tex], so the x coordinate is -1.
By comparing, we get m = -2.
So the slope is m = -2 and the coordinates of the point is (-1, 15) which is the first option.
