We will need to first find an equation in point-slope form. Which, we must first determine the slope. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#
Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.
Substituting the values from the two points in the problem gives:
#m = (color(red)(-2) - color(blue)(6))/(color(red)(3) - color(blue)(-1))#
#m = (color(red)(-2) - color(blue)(6))/(color(red)(3) + color(blue)(1))#
#m = -8/4 = -2#
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.
We can substitute the slope we calculated and the first point giving:
#(y - color(red)(6)) = color(blue)(-2)(x - color(red)(-1))#
#(y - color(red)(6)) = color(blue)(-2)(x + color(red)(1))#
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 point-slope form to this form:
#y - color(red)(6) = (color(blue)(-2) xx x) + (color(blue)(-2) xx color(red)(1))#
#y - 6 = -2x - 2#
#2x + y - 6 + 6 = 2x - 2x - 2 + 6#
#2x + y - 0 = 0 + 4#
#2x + y = 4#
