7. Intercept form

Let us find the equation of the straight line whose intercepts are $a$ and $b$ on the coordinate axes, respectively.

 

 

Let $PQ$ be a straight line that meets the $x$ - axis at the point $A$ and the $y$ axis at the point $B$. The coordinates of points $A$ and $B$ are $(a,0)$ and $(0,b)$, respectively. Then, $OA = a$ and $OB = b$.

 

Here, $(x_1,y_1) = (a,0)$ and $(x_2,y_2) = (0,b)$.

 

Substituting the known values in two point form equation, we get:

 

$\frac{y - 0}{b - 0} = \frac{x - a}{0 - a}$

 

$\frac{y}{b} = \frac{x - a}{-a}$

 

$\frac{y}{b} = \frac{-x}{a} + 1$

 

$\frac{x}{a} + \frac{y}{b} = 1$

 

Hence, the equation of the intercept of the line is $\frac{x}{a} + \frac{y}{b} = 1$.