First, we can write an equation in 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 given in the problem gives:
#(y - color(red)(4)) = color(blue)(-2/5)(x - color(red)(8))#
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 solve for this form as follows:
First, multiple each side of the equation by #color(green)(5)# to remove the fraction. In standard form both the coefficients and the constant must be integers:
#color(green)(5)(y - color(red)(4)) = color(green)(5) xx color(blue)(-2/5)(x - color(red)(8))#
#(color(green)(5) xx y) - (color(green)(5) xx color(red)(4)) = cancel(color(green)(5)) xx color(blue)(-2/cancel(5))(x - color(red)(8))#
#5y - 20 = -2(x - 8)#
Next, expand the terms on the right side of the equation:
#5y - 20 = (-2 xx x) - (-2 xx 8)#
#5y - 20 = -2x - (-16)#
#5y - 20 = -2x + 16#
Now, add #color(green)(20)# and #(color)(red)(2x)# to each side of the equation to put this equation in Standard Form:
#color(red)(2x) + 5y - 20 + color(green)(20) = color(red)(2x) - 2x + 16 + color(green)(20)#
#color(red)(2x) + 5y - 0 = 0 + color(green)(36)#
#color(red)(2)x + color(blue)(5)y = color(green)(36)#
