Question

L1 y= - 4/3x+3 and L2 y=5/4x-3

Are parallel, perpendicular, or intersecting (neither)?

Answer 1

the lines are intersecting

Explanation:

We can immediately eliminate the possibility of a parallel pair of lines because one of the slopes of the lines is negative guiding us towards the answer being perpendicular/intersecting. But the lines aren't perpendicular either. This is because of a pair of lines to be perpendicular, their slopes have to be the opposite of each other. For example, a perpendicular line for y= -4/3x+3 could be y=4/3x-3. The y intercept does not effect the lines from being perpendicular or parallel at all. So we conclude with the choice that the lines can only be intersecting.

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Answer 2

intersecting(neither)

Explanation:

Line L1: \[y = -4/3x + 3\]

Line L2: \[y = 5/4x - 3\]

The lines are represented in the format y = mx + c where m is the slope of the line and c is the intercept.

Hence slope of line L1 = -4/3

Slope of line L2 = 5/4

For the lines to be parallel, the slopes should be equal. But this is not the case here. Similarly, for the lines to be perpendicular, the product of the slopes should be -1. That is again not the case.

Hence we can conclude that the lines L1 and L2 are intersecting.