Question

Indicate in standard form the equation of the line passing through the given points.

G(4, 6), H(1, 5)

Answer 1

By slope formula m = (y - y1)/(x - x1), let:

(x,y) = (4,6)
(x1,y1) = (1,5)

So:

m = (6 - 5)/(4 - 1)
= 1/3

Then, by point-slope formula y - y1 = m(x - x1), letting m = 1/3 and (x1,y1) = (1,5):

y - 5 = 1/3 * (x - 1)

Since standard form consists of integers, multiply the expression by 3:

3(y - 5) = 1/3 * (x - 1) * 3
3y - 15 = x - 1

So in Ax + By = C form:

x - 3y - 1 = -15
x - 3y = -14 [Note that x must be positive integer!]