Question

Write the equation of line passing through $A(-3,4)$ and $B(4,5)$ in the form of $ax+by+c=0$.

Answer 1

We need to find the equation of the line passing through the points $A(-3,4)$ and $B(4,5)$.

The equation of the line is $\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}$

Here $(-3,4)\equiv (x_1,y_1),(4,5)\equiv (x_2,y_2)$

$\therefore \frac{x+3}{4+3}=\frac{y-4}{5-4}$

$\Rightarrow \frac{x+3}{7}=\frac{y-4}{1}$

$\Rightarrow x+3=7(y-4)$

$\Rightarrow x+3=7y-28$

$\Rightarrow x-7y+3+28=0$

$\Rightarrow x-7y+31=0$