Question

Write the equation of the line passing through the pair of points $(2,3)$ and $(4,7)$ in the form of $y=mx+c$.

Answer 1

Here, $(2,3)=(x_1,y_1)$ and $(4,7)=(x_2,y_2)$
Equation of line passing through the point (2, 3) and (4, 7) is.
$\frac{y-y_1}{x-x_1}=\frac{y_1-y_2}{x_1-x_2}$
$\Rightarrow \frac{y-3}{x-2}=\frac{3-7}{2-4}=\frac{-4}{-2}$
$\Rightarrow y-3=2(x-2)$
$\Rightarrow y-3=2x-4$
$\therefore y=2x-1$ which is in the form $y=mx+c$ is the required equation.