Question:
Slope of a line which cuts off intercepts of equal lengths on the axes is
A. – 1
B. – 0
C. 2
D. √3
Solution:
A. – 1
Explanation:
We know that the equation of line in intercept form is
$\frac{x}{a}+\frac{y}{b}=1$
Where $\mathrm{a}$ and $\mathrm{b}$ are the intercepts on the axis.
Given that $\mathrm{a}=\mathrm{b}$
$\Rightarrow \frac{x}{a}+\frac{y}{a}=1$
$\Rightarrow \frac{x+y}{a}=1$
$\Rightarrow x+y=a$
$\Rightarrow y=-x+a$
$\Rightarrow y=(-1) x+a$
Since, the above equation is in $\mathrm{y}=\mathrm{mx}+\mathrm{b}$ form So, the slope of the line is $-1$.