First, we need to 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 problem gives:
#m = (color(red)(-3) - color(blue)(3))/(color(red)(-2) - color(blue)(-8)) = (color(red)(-3) - color(blue)(3))/(color(red)(-2) + color(blue)(8)) = (-6)/6 = -1#
Now, we can use the point-slope formula to find the equation for the line through these points. 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 first point gives:
#(y - color(red)(3)) = color(blue)(-1)(x - color(red)(-8))#
#(y - color(red)(3)) = color(blue)(-1)(x + color(red)(8))#
Or, we can substitute the slope we calculated and the second point giving:
#(y - color(red)(-3)) = color(blue)(-1)(x - color(red)(-2))#
#(y + color(red)(3)) = color(blue)(-1)(x + color(red)(2))#
