Question

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).

Answer 1

The line cuts off equal intercepts on the coordinate axes and passes through the point ( 2,3 ) .

The formula for the equation of a line which makes an intercept of a and b unit on the x- axis and y- axis respectively is given by,

x a + y b =1 (1)

Since it is given that the line cuts off equal intercepts.

a=b (2)

Substitute the value of a from equation (2) to equation (1).

x b + y b =1 x+y=b (3)

As the line passes through the point ( 2,3 ) it satisfies the equation of line.

Substitute the value of ( x,y ) as ( 2,3 ) in equation (3).

2+3=b b=5

Substitute the value of b in equation (3).

x+y=5

Thus, the equation of line cuts off equal intercepts on the coordinate axes and passes through the point ( 2,3 ) is x+y=5 .