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 equation gives:
#m = (color(red)(-3) - color(blue)(5))/(color(red)(-1) - color(blue)(5))#
#m = (-8)/-6 = (-2 xx 4)/(-2 xx 3)= (cancel(-2) xx 4)/(cancel(-2) xx 3) = 4/3#
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 to give:
#(y - color(red)(5)) = color(blue)(4/3)(x - color(red)(5))#
We also can substitute the slope we calculated and the second point to give:
#(y - color(red)(-3)) = color(blue)(4/3)(x - color(red)(-1))#
#(y + color(red)(3)) = color(blue)(4/3)(x + color(red)(1))#
