Parallel and Perpendicular lines from equation

Question

What do the following two equations represent?

4x-2y=-5

Y=-1/2x1/10

Answer 1

I don't know how to interpret: y = –1/2x1/10

However, the slope appears to be –1/2 regardless of what the rest of the equation represents.

The slope of the other line can be determined if we rewrite the equation in slope-intercept form.

4x — 2y = –5

4x – 2y + 5 = –5 + 5

4x – 2y + 5 = 0

4x –2y + 5 + 2y = 0 + 2y

4x + 5 = 2y

2x + (5/2) = y

So, we can see that the slope of the first line is 2, since 2 is the coefficient of the x-term when the equation is written in the "y=" form.

When one line has a slope that is the negative reciprocal of the slope of another line, those lines are PERPENDICULAR, meaning they cross at right angles or at 90° angles.

2 and –1/2 are NEGATIVE RECIPROCALS of each other. Thus, the two lines that were given us are PERPENDICULAR to each other. By the way, PARALLEL lines have the same slope.

Answer 2

4x -2y = -5

-2y = -4x - 5

2y = 4x + 5

y = 2x + 5/2

slope = 2

y = -1/2x 1/10

must be a typo here, but slope is -1/2

product of two slopes is -1 so the lines are perpendicular