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

With two points given, first find the slope between them, then apply the point-slope (or equivalently two-point) form using either of the two given points.

First compute the slope through the two given points $(1,2)$ and $(3,8)$:

Now apply point-slope form using $(x_1,y_1)=(1,2)$:

In general form:

$3x - y - 1 = 0$ …

As an alternative, using two-point form directly: $y-2 = \dfrac{8-2}{3-1}(x-1) = 3(x-1)$, which is identical to the point-slope calculation above — two- …

Computing the slope as $\dfrac{3-1}{8-2}$ (inverting numerator and denominator) is a very common error — always keep $\dfrac{y_2-y_1}{x_2-x_1}$ in that exact order. Also remember to check the …