First, we can use the point-slope formula to write an equation for the line. The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#
Where #color(blue)(m)# is the slope and #(color(red)(x_1, y_1))# is a point the line passes through.
Substituting the slope and values from the point in the problem gives:
#(y - color(red)(5)) = color(blue)(-3)(x - color(red)(1))#
We can now solve for the Standard Form of the equation. 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
#y - color(red)(5) = (color(blue)(-3) xx x) - (color(blue)(-3) xx color(red)(1))#
#y - color(red)(5) = -color(blue)(3)x - (-3)#
#y - color(red)(5) = -color(blue)(3)x + 3#
#y - color(red)(5) + 5 = -color(blue)(3)x + 3 + 5#
#y - 0 = color(blue)(3)x + 8#
#3x + y = 3x + color(blue)(3)x + 8#
#3x + y = 0 + 8#
#color(red)(3)x + color(blue)(1)y = color(green)(8)#
