Question

State whether the slopes would represent parallel lines, perpendicular lines, or neither.

-4 and 1/4
8 and -8
7 and 17
2 and 2

Answer 1

neither

Explanation:

i am goung to assume that the quarter really is just a quarter unit on the y-axis

Answer 2

The line with a slope of
`(-4)` is perpendicular to the line with a slope of
`(1/4)` since the product of the two slopes is
`(-1)`.

Slope of
`8` and slope of
`(-8)`: neither parallel nor perpendicular.

Slope of
`7` and slope of
`17`: neither parallel nor perpendicular.

The line with a slope of
`2` is parallel to the other line of slope
`2\!` since the two lines have the same slope.

Explanation:

Two lines in a cartesian plane are parallel to one another if and only if their slopes are equal. Two lines in a cartesian plane are perpendicular to one another if and only if the product of their slopes is
`(-1)`.

For example, a line with a slope of
`m` is parallel to another line of the same slope,
`m\!`.

Since
`(-m)\, (1/m) = -1`, a line with a slope of
`(-m)` would be perpendicular to a line of slope
`(1/m)`.