A line passes through the point `(10,-2)` and forms with the axes a triangle of area of 9 sq units. Find the equation of the line.

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Denote the slope of this line as `m.` The vertical line (which has an undefined slope) doesn't suit us, so we'll not miss a solution. Horizontal line with `m=0` doesn't suit also, so we can divide by `m.`

The equation of such a line is `y = m*(x-10) - 2.` The triangle formed with this line and the axes is a right one (because the axes are perpendicular to each other). So its area is `1/2 * |OX| * |OY|,` where `O` is the origin, `X` is...

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