First we must 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 points in the equation gives:
#m = (color(red)(8) - color(blue)(-1))/(color(red)(-6) - color(blue)(-3))#
#m = (color(red)(8) + color(blue)(1))/(color(red)(-6) + color(blue)(3))#
#m = 9/-3 = -3#
We can now use the calculated slope and the first point to write an equation in the 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. Substitution gives:
#(y - color(red)(-1)) = color(blue)(-3)(x - color(red)(-3))#
#(y + color(red)(1)) = color(blue)(-3)(x + color(red)(3))#
We can now solve for #y# to put the equation in slope intercept form.
#y + color(red)(1) = (color(blue)(-3) xx x) + (color(blue)(-3) xx color(red)(3))#
#y + color(red)(1) = -3x - 9#
#y + color(red)(1) - 1 = -3x - 9 - 1#
#y = -3x - 10#
