First, determine the slope of the line. 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 points in the problem gives:
#m = (color(red)(-2) - color(blue)(-5))/(color(red)(-4) - color(blue)(-1)) = (color(red)(-2) + color(blue)(5))/(color(red)(-4) + color(blue)(1)) = 3/-3 = -1#
Next, 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 calculate slope and the values from the first point in the problem gives:
#(y - color(red)(-5)) = color(blue)(-1)(x - color(red)(-1))#
#(y + color(red)(5)) = color(blue)(-1)(x + color(red)(1))#
We can now transform this to the Standard Linear form. 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
#y + color(red)(5) = (color(blue)(-1) * x) + (color(blue)(-1) * color(red)(1))#
#y + color(red)(5) = color(blue)(-1x) - 1#
#1x + y + color(red)(5) - 5 = 1x color(blue)(- 1x) - 1 - 5#
#1x + y + 0 = 0 - 6#
#color(red)(1)x + color(blue)(1)y = color(green)(-6)#
