First, 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 problem gives:
#m = (color(red)(3) - color(blue)(-3))/(color(red)(2) - color(blue)(4))#
#m = (color(red)(3) + color(blue)(3))/(color(red)(2) - color(blue)(4))#
#m = 6/-2#
#m = -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 values from one of the points in the problem and the slope we calculated gives:
#(y - color(red)(-3)) = color(blue)(-3)(x - color(red)(4))#
#(y + color(red)(3)) = color(blue)(-3)(x - color(red)(4))#
Substituting the values from one the other points in the problem and the slope we calculated gives:
#(y - color(red)(3)) = color(blue)(-3)(x - color(red)(2))#
