First, we must 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)(2) - color(blue)(-4))/(color(red)(4) - color(blue)(-5))#
#m = (color(red)(2) + color(blue)(4))/(color(red)(4) + color(blue)(5)) = 6/9 = (3 xx 2)/(3 xx 3) = (color(red)(cancel(color(black)(3))) xx 2)/(color(red)(cancel(color(black)(3))) xx 3) = 2/3#
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.
We can substitute the slope we calculated and the first point giving:
#(y - color(red)(-4)) = color(blue)(2/3)(x - color(red)(-5))#
#(y + color(red)(4)) = color(blue)(2/3)(x + color(red)(5))#
We can also substitute the slope we calculated and the second point giving:
#(y - color(red)(2)) = color(blue)(2/3)(x - color(red)(4))#
