First, we need to determine the slope of the equation. 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)(-2))/(color(red)(-3) - color(blue)(9)) = (color(red)(2) + color(blue)(2))/(color(red)(-3) - color(blue)(9)) = 4/-12 = -1/3#
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 we calculated and the values from the first point in the problem gives:
#(y - color(red)(-2)) = color(blue)(-1/3)(x - color(red)(9))#
#(y + color(red)(2)) = color(blue)(-1/3)(x - color(red)(9))#
We can also substitute the slope we calculated and the values from the second point in the problem giving:
#(y - color(red)(2)) = color(blue)(-1/3)(x - color(red)(-3))#
#(y - color(red)(2)) = color(blue)(-1/3)(x + color(red)(3))#
