First, we need to determine the slope of the line passing through these two points.
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 problem gives:
#m = (color(red)(5) - color(blue)(3))/(color(red)(-2) - color(blue)(-1))#
#m = (color(red)(5) - color(blue)(3))/(color(red)(-2) + color(blue)(1))#
#m = 2/-1 = -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 and the first point from the problem to give:
#(y - color(red)(3)) = color(blue)(-2)(x - color(red)(-1))#
#(y - color(red)(3)) = color(blue)(-2)(x + color(red)(1))#
We can also substitute the slope and the second point from the problem to give:
#(y - color(red)(5)) = color(blue)(-2)(x - color(red)(-2))#
#(y - color(red)(5)) = color(blue)(-2)(x + color(red)(2))#
