First, we can write an equation in the point-slope form. 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)(-2)) = color(blue)(2)(x - color(red)(-3))#
#(y + color(red)(2)) = color(blue)(2)(x + color(red)(3))#
We can now transform this equation into the Standard Linear form. 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)(2) = (color(blue)(2) xx x) + (color(blue)(2) xx color(red)(3))#
#y + color(red)(2) = 2x + 6#
#y + color(red)(2) - 2 = 2x + 6 - 2#
#y + 0 = 2x + 4#
#y = 2x + 4#
#-color(red)(2x) + y = -color(red)(2x) + 2x + 4#
#-2x + y = 0 + 4#
#-2x + y = 4#
#color(red)(-1)(-2x + y) = color(red)(-1) xx 4#
#(color(red)(-1) xx -2x) + (color(red)(-1) xx y) = -4#
#color(red)(2)x - color(blue)(1)y = color(green)(-4)#
