Question

A line passes through $(x_1,y_1)\text{and}(h,k).$ If slope of the line is $m$, show that $k–y_1=m(h–x_1)$.

Answer 1

We know that slope of a line through the points $(x_1,y_1)\text{and}(x_2,y_2)\text{is}m=\frac{y_2-y_1}{x_2-x_1}$

So, Slope of line passing through $(x_1,y_1)\text{and}(h,k)=\frac{k-y_1}{h-x_1}$
$\therefore m=\frac{k-y_1}{h-x_1}$
$m(h-x_1)=k-y_1$
$k-y_1=m(h-x_1)$
Hence proved.