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 the values from the point in the problem gives.
#(y - color(red)(2)) = color(blue)(-2)(x - color(red)(4))#
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 transform the point-slope equation to standard form as follows:
#y - color(red)(2) = (color(blue)(-2) * x) - (color(blue)(-2) * color(red)(4))#
#y - color(red)(2) = -2x + 8#
#color(blue)(2x) + y - color(red)(2) + 2 = color(blue)(2x) - 2x + 8 + 2#
#2x + y - 0 = 0 + 10#
#color(red)(2)x + color(blue)(1)y = color(green)(10)#
