y-7=4(x+4)
This is in the format of y-y_1= m(x-x_1) which is known as the point-slope form. To change this to standard form (Ax+By=C), you need to find the values of the points (x_1,y_1) and the slope (m):
y-7=4(x+4)
y-y_1= m(x-x_1)
Therefore,
(x_1,y_1) = (-4, 7) and m=4
y-7=4(x+4)
Now simplify and rearrange to get x and y terms on one side and constants on the other side of equal sign:
y-7=4(x+4)
y-7=4x+16
y=4x+16+7
y=4x+23
-4x+y=23
This is almost in the format of Ax+By=C but Ax cannot have a negative sign in front of it. To get rid of this negative, divide both sides of the equation by -1:
(-4x+y)/-1=23/-1
4x-y=-23
Now the equation is in standard form because A=4, B=-1 and C=-23.