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

$<b>Answer :-</b>$

x + y = 11

$<b>Step-by-step explanation :</b>$

We know that,


➡️ a and b coordinates on axis is :-
↪️ x/a + y/b = 1

We also know that,

➡️ x intercept = y intercept

⛬, y = b

⛬, Equations

➡️ x/a + y/a = 1

➡️ x + y = a-----(1)

Given :- (4,7)

➡️ Put the value in equation 1

➡️ 4 + 7 =a

So,

➡️ a = 11

⛬, the equation will be $<b> x + y = 11</b>$



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