What lines can't be expressed using the form (x/a) + (y/b) = 1?

Question

Three types -- and it would be helpful if you could explain why. :-) Thanks!

Answer 1

1. Horizontal lines

2. Vertical lines

3. Lines through the origin

A horizontal line has the equation y = k, for some real number k. This equation can't be written in the form you gave.

A vertical line has the equation x = k, for some real number k. This equation can't be written in the form you gave.

The equation of a line through the origin has to have (0, 0) as a solution. But in your equation, plugging in x = 0 and y = 0 won't make your equation true.

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As it happens, any other line can be written in the form you listed. If you have a line y = mx + b, where b and m are nonzero, then it isn't hard to convert this line to the form you want--just subtract mx from both sides and divide by b.

Answer 2

anything where a or b are 0