First, because we are given a point and the slope we can find an equation using the point-slope formula.
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)(-5)) = color(blue)(-2)(x - color(red)(-6))#
#(y + color(red)(5)) = color(blue)(-2)(x + color(red)(6))#
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 our equation into this format.
#y + color(red)(5) = (color(blue)(-2) xx x) + (color(blue)(-2) xx color(red)(6))#
#y + color(red)(5) = -2x - 12#
#y + color(red)(5) - 5 + color(blue)(2x) = -2x - 12 - 5 + color(blue)(2x)#
#y + color(red)(5) - 5 + color(blue)(2x) = -2x - 12 - 5 + color(blue)(2x)#
#2x + y + 0 = 0 - 17#
#color(red)(2)x + color(blue)(1)y = color(green)(-17)#
