Question

Find the equation to the straight line which passes through the point $(5,6)$ and has intercepts on the axes
(i) equal in magnitude and both positive.
(ii) equal in magnitude but opposite in sign.

Answer 1

$\left(1\right)$ Let the x intercept and y intercept both be 'a'.

The equation is $\frac{x}{a}+\frac{y}{a}=1$

(or) $x+y=a$

The line passes through $(5,6)$

Hence $5+6=a$

(or) $a=11$

$\therefore$ Equation of the line is $x+y=11$.

$\left(2\right)$ Let the x intercept be 'a' and y intercept be 'b'.

Given that they are of equal magnitude but opposite in sign.

$\therefore b=-a$

Equation is $\frac{x}{a}-\frac{y}{a}=1$

or $x-y=0$

Line passes through $(5,6)$

$5-6=a$

$a=-1$

$\therefore$ The equation of the line is $x-y+1=0$.