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# Slope of a line which cuts off intercepts

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 $-1$.