So you have y-y1=m(x-x1) and you are told that the slope has to be parallel to the line x-2y=6
1.) solve x-2y=6 for y
x-2y=6
Subtract x from both sides to get
-2y=6-x
Divide each side by -2 to get
y=-3-(x/2)
Now the slope for this equation is -1/2 and the line has to be parallel to this equation. Therefore the slope of the line that is parallel to this equation is going to be -1/2.
Now You have to use the point (2,-5) as your x1 and y1 and the slope that is parallel to the line x-2y=6, which is -1/2
y-(-5)=-1/2[x-(-2)]
Simplifying this you get
y+5=-1/2(x+2)
Above is how you write the equation in point slope form.
Now if it is asking you for slope-intercept form all you do is distribute -1/2 and subtract 5
y+5=-1/2(x+2)
y+5=-1x/2-1
Subtracting 5 from both sides gives you
y=-x/2 +4. Hope this helps. Let me know if you have questions