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 problem gives:
#m = (color(red)(-3) - color(blue)(4))/(color(red)(4) - color(blue)(-3)) = (color(red)(-3) - color(blue)(4))/(color(red)(4) + color(blue)(3)) = -7/7 = -1#
We can now use the point-slope formula to write the equation for the line. 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 slope we calculated and the values from the first point in the problem gives:
#(y - color(red)(4)) = color(blue)(-1)(x - color(red)(-3))#
#(y - color(red)(4)) = color(blue)(-1)(x + color(red)(3))#
Or
#(y - color(red)(4)) = color(blue)(-)(x + color(red)(3))#
We can also substitute the slope we calculated and the values from the second point in the problem giving:
#(y - color(red)(-3)) = color(blue)(-1)(x - color(red)(4))#
#(y + color(red)(3)) = color(blue)(-1)(x - color(red)(4))#
Or
#(y + color(red)(3)) = color(blue)(-)(x - color(red)(4))#
