Question

state whether the lines represented by the equations y=1/2x-1 and y+4=-1/2(x-2) are paraller, perdendicular, or neither

Answer 1

The easiest way to tell whether lines are parallel, perpendicular, or neither is when they are written in slope-intercept form or y = mx + b. We will begin by putting both of our equations into this format.

The first equation, $y = \frac{1}{2}x - 1$ is already in slope intercept form. The slope is 1/2 and the y-intercept is -1.

The second equation requires rearranging.
$y + 4 = -\frac{1}{2}(x - 2) \\ y + 4 = -\frac{1}{2}x + 1 \\ y = - \frac{1}{2} x- 3$
From this equation, we can see that the slope is -1/2 and the y-intercept is -3.

When lines are parallel, they have the same slope. This is not the case with these lines because one has slope of 1/2 and the other has slope of -1/2. Since these are not the same our lines are not parallel.

When lines are perpendicular, the slope of one is the negative reciprocal of the other. That is, if one had slope 2, the other would have slope -1/2. This also is not the case in this problem.

Thus, we conclude that the lines are neither parallel nor perpendicular.