Question

Indicate in standard form the equation of the line passing through the given points G (4,6) H (1,5)

Answer 1

First, find the slope (m) =
`(y2 - y1)/(x2 - x1)` =
`(5 - 6)/(1 - 4)` =
`(-1)/(-3)` =
`(1)/(3)`

Now plug in ONE of the points and the slope into the point-slope equation:

y - y₁ = m(x - x₁); where (x₁, y₁) is the chosen point.

y - 5 =
`(1)/(3)`(x - 1) (I used (1,5) as the chosen point)

3(y - 5) = x - 1

3y - 15 = x - 1

3y -14 = x

-14 = x - 3y → x - 3y = -14

Answer: x - 3y = -14