Question

What is the equation of the line, in slope-intercept form, that passes through (3, -1) and (-1, 5)?

Answer 1

Using the point-slope form (y - y₁) = m (x - x₁)

m= gradient = Δy/Δx

=
`(5 - (-1))/((-1) - 3)`

= -
`(3)/(2)`

midpoint of the line =
`( (x_(1) + x_(2) )/(2) , (y_(1) + y_(2) )/(2))`
=
`(\frac{3 + (-1)} {2} , (-1 + 5 )/(2))`

= (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 =
`(3)/(2)x - (3)/(2)`

⇒
`y - (3)/(2) x = (4)/(2) - (3)/(2)`

⇒
`y - (3)/(2) x = (1)/(2)`

by multiplying through by 2,

⇒ 2y - 3x = 1