Question

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

Answer 1

To find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3), we can start by noting that if a line cuts off equal intercepts, we can express the equation of the line in the form:

\[
x + y = c
\]

where \(c\) is the length of the intercepts on the axes. Since both intercepts are equal, we can also express the intercepts as \(\frac{c}{2}\) on both the x-axis and y-axis.

Next, we need this line to pass through the point (2, 3). Thus, we can substitute \(x = 2\) and \(y = 3\) into the equation \(x + y = c\):

\[
2 + 3 = c
\]

This gives us:

\[
c = 5
\]

Now, we can substitute \(c\) back into the line equation:

\[
x + y = 5
\]

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

In summary, the equation of the line is:

\[
\boxed{x + y = 5}
\]