#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#.