First, we can use the point-slope formula to write and equation for the line. The point-slope form of a linear equation is: #(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))#
Where #(color(blue)(x_1), color(blue)(y_1))# is a point on the line and #color(red)(m)# is the slope.
Substituting the slope from the problem and the values from the point in the problem gives:
#(y - color(blue)(-1)) = color(red)(-2)(x - color(blue)(3))#
#(y + color(blue)(1)) = color(red)(-2)(x - color(blue)(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 now solve for this format as follows:
#y + color(blue)(1) = (color(red)(-2) xx x) - (color(red)(-2) xx color(blue)(3))#
#y + color(blue)(1) = -2x - (-6)#
#y + color(blue)(1) = -2x + 6#
#color(red)(2x) + y + color(blue)(1) - 1 = color(red)(2x) - 2x + 6 - 1#
#2x + y + 0 = 0 + 5#
#color(red)(2)x + color(blue)(1)y = color(green)(5)#
