Question

Use words and algebraic statements only to help me answer the question:

1. By looking at two linear equations, how can you tell that the corresponding lines are parallel? Please explain with an example.

Answer 1

You can see that two functions dependent on x and y are parallel if the coefficients of x and y of the first function are directly proportional to those of x and y of the second function.

Example:

These functios are all parallel.

Set f(x,y) = 0 and solve for y. You'll get

The slope is the same for all equations. Also, if the slope s1 = -(s2), the lines are also parallel. Parallel lines must have the same magnitude of slope.