We can use the point slope formula to first find an equation for this 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 values from the problem gives:
#(y - color(red)(6)) = color(blue)(-2)(x - color(red)(-3))#
#(y - color(red)(6)) = color(blue)(-2)(x + color(red)(3))#
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
We can convert the point-slope form to the standard form as follows:
#y - color(red)(6) = (color(blue)(-2) xx x) + (color(blue)(-2) xx color(red)(3))#
#y - color(red)(6) = -2x - 6#
#color(blue)(2x) + y - color(red)(6) + 6 = color(blue)(2x) - 2x - 6 + 6#
#2x + y - 0 = 0 - 0#
#color(red)(2)x + color(blue)(1)y = color(green)(0)#
