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

The point where the line or curve crosses the axis of the graph is called intercept. If a point crosses the x-axis, then it is called the x-intercept. If a point crosses the y-axis, then it is called the y-intercept.

## Intercept Formula

The equation of the line, which intersects the y-axis at a point is given by:
y = mx + c
Now, we have to write the intercept form of the line, we can replace c with b. Thus, the equation becomes:

y = mx + b
Hence, the formula for the y-intercept of a line is given by:
b = y – mx
Where b is the intercept, m is the slope of the line and y and x indicate the points on the y-axis and x-axis respectively.

Now, another way of writing the equation of the line, considering a line is intersecting the x-axis and y-axis at points a and b respectively.
x/a + y/b = 1
Here, a and b are the intercepts of the line which intersect the x-axis and y-axis, respectively. The values of a and b can be positive, negative or zero and explain the position of the points at which the line cuts both axes, relative to the origin.

### Solution

The line cuts off equal intercepts on the coordinate axes i.e. a = b.

We know that equation of the line intercepts a and b on the x-and y-axis, respectively, which is

x/a + y/b = 1

So, x/a + y/a = 1

x + y = a … (1)

Given: point (2, 3)

2 + 3 = a

a = 5

Substitute value of ‘a’ in (1), we get

x + y = 5

x + y – 5 = 0

∴ The equation of the line is x + y – 5 = 0.

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