Question

The equation of the straight line passing through the point (1,2) and making equal angle with the axes

Answer 1

any line through (1,2) is...

$y - 2 = m(x - 1)$

since line make equal angle with axes so lenght of intercept on both axes must be equal...

$mx - y = m - 2 \\ \frac{mx}{(m - 2)} + \frac{y}{ - (m - 2)} = 1 \\ \frac{x}{m(m - 2)} + \frac{y}{ - (m - 2)} = 1$

$now... \\ m(m - 2) = - (m - 2) \\ m(m - 2) + (m - 2) = 0 \\ (m - 2)(m + 1) = 0 \\ \\ m = - 1 \: and \: 2$