The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#
Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
The slope of an equation in standard form is: #m = -color(red)(A)/color(blue)(B)#
Therefore we can write:
#5/4 = -color(red)(A)/color(blue)(B)#
Or
#-5/-4 = -color(red)(A)/color(blue)(B)#
So #color(red)(A) = 5# and #color(blue)(B) = -4#
We can substitute this into the formula to give:
#color(red)(5)x + color(blue)(-4)y = color(green)(C)#
#color(red)(5)x - color(blue)(4)y = color(green)(C)#
We can now substitute the values from the point in the problem for #x# and #y# and solve for #color(green)(C)#:
#(color(red)(5) * 4) - (color(blue)(4) * -8) = color(green)(C)#
#20 - (-32) = color(green)(C)#
#20 + 32 = color(green)(C)#
#52 = color(green)(C)#
Substituting this gives the result:
#color(red)(5)x - color(blue)(4)y = color(green)(52)#
