Using the point-slope form (y - y₁) = m (x - x₁)
m= gradient = Δy/Δx
= [tex] \frac{5 - (-1)}{(-1) - 3} [/tex]
= -[tex] \frac{3}{2} [/tex]
midpoint of the line = [tex]( \frac{x_{1} + x_{2} }{2} , \frac{y_{1} + y_{2} }{2})[/tex]
= [tex](\frac{3 + (-1)} {2} , \frac{-1 + 5 }{2}) [/tex]
= (1 , 2)
Using the formula, plug in the values for m = 3/2, y₁= 2 , x₁= 1
(y - 2) = 3/2 (x - 1)
y - 2 = [tex] \frac{3}{2}x - \frac{3}{2} [/tex]
⇒ [tex]y - \frac{3}{2} x = \frac{4}{2} - \frac{3}{2}[/tex]
⇒ [tex]y - \frac{3}{2} x = \frac{1}{2} [/tex]
by multiplying through by 2,
⇒ 2y - 3x = 1
