Please let me know if this is correct:
Find the equation of the line which satisfies the point through the point (0,5) with slope =-2
y-y1 = m(x-1)=
y-5=-2(x-1)=
y=-2x+-7
Perhaps you meant it, but it should be: $\displaystyle y - y_1 = m\left( {x - x_1 } \right)$.
Now, with m = -2 and the point being (0,5) we get:
$\displaystyle y - 5 = - 2\left( {x - 0} \right) \Leftrightarrow y - 5 = - 2x \Leftrightarrow y = - 2x + 5$
The slope is clearly fine and you can easily check whether the line goes through the given point by filling it in to see if it satisfies the equation.