Question

Slope of a line which cuts intercepts of equal lengths on the axes is
A) $-1$
B) $0$
C) $2$
D) $\sqrt{3}$

Answer 1

In this problem, we have to use the equation of line in intercept form that is $\dfrac{x}{a}+\dfrac{y}{b}=1$ and in question it has been mentioned that slope of line cuts intercepts of equal length on the axis that means $a=b$ substitute this values and further simplifying this we get the value of slope by comparing with general equation of line that is $y=mx+c$. Now, solve it further and get the slope of the line.

Complete step by step answer:
In this type of problem, we have to write in equation of line in intercept form that is $\dfrac{x}{a}+\dfrac{y}{b}=1--(1)$
If you see in this question then it has been mentioned that slope of line cuts the intercept of equal length of axes that means $a=b$and substituting this values in equation (1) we get:
$\dfrac{x}{a}+\dfrac{y}{a}=1$
From the above equation we have to write in the form of straight line equation to find the slope of line for that first we need to take LCM of this above equation we get:
$\dfrac{x+y}{a}=1$
Multiply by a on both sides that is
$a\times \dfrac{x+y}{a}=a$
By simplifying further we get:
$x+y=a$
By rearranging the term we get:
$y=-x+a$
By comparing with $y=mx+c$
We get the slope of a line that is $m=-1$
Therefore, the correct option is option (A).

Note:
In this problem, remember the equation of line in intercept form and another condition which is given that slope of line cuts the intercept of equal length of axes that means $a=b$ and after simplifying further we get the value of slope by comparing it with straight line equations. By comparing we must compare with the coefficient to find the slope of a line.