Question

Find the equation of the line that cuts of equal Intercepts on the co-ordinate axes and passes through the point(4,7) please solution

Answer 1

We know,

equation of a line which makes intercepts of length a and b on the coordinate axes is :-

$\frac{x}{a} + \frac{y}{b} = 1$

Here, x intercept = y intercept

=> a = b.

So, the equation of the line becomes :-

$\frac{x}{a} + \frac{y}{a} = 1 \\ = > x + y = a$........(i)

Now, given this line passes through (4,7).So,it will satisfy the equation ....(i)

4 + 7 = a.

Hence, a = 11.

So,the equation of line will be x + y = a.

x + y = 11.

Regards

KSHITIJ

Answer 2

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Intercept form of Equation

x intercept = y intercept

Therefore

= $\bf\huge\frac{x}{a}$ + $\bf\huge\frac{y}{b}$

=> a = b.

$\bf\huge\frac{x}{a}$ + $\bf\huge\frac{y}{a} = 1$

=> x + y = a

Now given

x + y -a = 0

4 + 7 - a = 0

Therefore

a = 11.

Equation of line :-

x + y = a.

x + y = 11.

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