Q.Find the equation of the line which passes through the point $(1, 4)$ and has slope $2$.

A point and a slope call for the point-slope form $y - y_1 = m(x - x_1)$.

Given a point $(x_1, y_1)$ and the slope $m$, the point-slope form of the line is

With $(x_1, y_1) = (1, 4)$ and $m = 2$:

In general form this is $2x - y + 2 = 0$. …

Alternatively use slope–intercept form: with $m = 2$, write $y = 2x + c$, then substitute the point $(1,4)$ to find $c$: $4 = 2(1) + …

Expanding $2(x-1)$ as $2x - 1$ (forgetting to multiply the $1$ by $2$) is the usual slip. Distribute t …