Find the equation using the points (2,3) and (5,8)

The equation of the line that passing through 2 given
points is:

(x2 - x1)/(x - x1) = (y2 - y1)/(y -
y1)

We'll identify x1 = 2, x2 = 5, y1 = 3 , y2 =
8.

We'll substitute them into the
formula:

(5 - 2)/(x - 2) = (8 - 3)/(y -
3)

3/(x - 2) = 5/(y - 3)

We'll
cross multiply:

5(x - 2) = 3(y -
3)

We'll remove the
brackets:

5x - 10 = 3y -
9

We'll add 9 both sides:

3y =
5x - 10 + 9

3y = 5x - 1

We'll
divide by 3:

y = 5x/3 -
1/3

The equation of the line that passing
through the points (2,3) and (5,8) is:

y = 5x/3 -
1/3