Find the equation of the line and cuts off equal intercepts

To Find: The equation of the line with equal intercepts on the coordinate axes and that passes through the point (4,7). 

Given : Let a and b be two intercepts of x-axis and y-axis respectively.

Also, given that two intercepts are equal, i.e., $a=b$

And $(4,7)$ passes through the point $(x, y)$

Formula used:

Now since intercept form of a line is given:

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

$\frac{4}{a}+\frac{7}{b}=1$

$\frac{4+7}{a}=1$

$a=11=b$

Therefore, The required Equation of the line is $\frac{x}{11}+\frac{y}{11}=1$

⟹ x + y = 11