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 our two points gives:
#m = (color(red)(-1) - color(blue)(-2))/(color(red)(2) - color(blue)(-3))#
#m = (color(red)(-1) + color(blue)(2))/(color(red)(2) + color(blue)(3))#
#m = 1/5#
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 values from the two points given in the problem and the slope we calculated results in:
#(y - color(red)(-2)) = color(blue)(1/5)(x - color(red)(-3))#
#(y + color(red)(2)) = color(blue)(1/5)(x + color(red)(3))#
or
#(y - color(red)(-1)) = color(blue)(1/5)(x - color(red)(2))#
#(y + color(red)(1)) = color(blue)(1/5)(x - color(red)(2))#
