Question

3 Find the equation of a line which
passes through (5,7), and makes equal
intercepts equal in magnitude but
opposite in sign with the axes.​

Answer 1

SOLUTION

TO DETERMINE

The equation of a line which passes through (5,7) and makes intercepts on the axes equal in magnitude but opposite in sign

EVALUATION

Here it is given that the line makes intercepts on the axes equal in magnitude but opposite in sign

Let the equation of the required line is

\displaystyle \sf{ \frac{x}{a} + \frac{y}{ - a} = 1}

a

x

+

−a

y

=1

Which can be rewritten as

\displaystyle \sf{ x - y = a} \: \: \: ......(1)x−y=a......(1)

Now the line given by the equation (1) passes through the point (5,7)

So the point (5,7) satisfies the equation (1)

\therefore \: \sf{5 - 7 = a}∴5−7=a

\implies \sf{a = - 2}⟹a=−2

Hence the required equation of the line is

\sf{x - y = - 2}x−y=−2

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Step-by-step explanation:

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