Q.Find the equation of the line passing through the points $(1, 2)$ and $(3, 8)$.

Two points call for the two-point form; first find the slope, then use point-slope with either point.

The two-point form of the line through $(x_1, y_1)$ and $(x_2, y_2)$ is

First compute the slope with $(1,2)$ and $(3,8)$:

Now apply the point-slope form using the point $(1, 2)$:

In general form: $3x - y - 1 = 0$. …

Computing the slope with mismatched order ($\tfrac{8-2}{1-3} = -3$) or substituting into the two-point form with the coordinates of one point split between the two bracke …