The slope of a line which cuts off intercepts | vedclass

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Question

(A) Let the intercepts cut by the line on the axes be $a$ and $a$ (since they are of equal length). Using the intercept form of the equation of a line

Vedclass · Accepted Answer

-$1$

Vedclass · Answer

(A) Let the intercepts cut by the line on the axes be $a$ and $a$ (since they are of equal length). Using the intercept form of the equation of a line: $\frac{x}{a} + \frac{y}{a} = 1$. Multiplying by $a$,we get $x + y = a$,or $x + y - a = 0$. The equation is in the form $Ax + By + C = 0$,where $A = 1$ and $B = 1$. The slope $m$ of the line is given by $m = -\frac{A}{B} = -\frac{1}{1} = -1$. Alternatively,if the intercepts are equal in magnitude but opposite in sign,the slope could be $1$. However,given the options,the standard interpretation is equal intercepts $a$,leading to a slope of $-1$.

The slope of a line which cuts off intercepts of equal lengths on the axes is:

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