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Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither.

y = 4x + 3
4x + y = 3

User Anniepoo
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1 Answer

4 votes

Answer: neither

Explanation:

For a graph to be parallel, it must have the same slope.

e.g., y = 2x and y = 2x + 1 are parallel because they both have the slope "2"

For a graph to be perpendicular, its slopes must be the reciprocal of each other, and the sign (positive/negative) is flipped

e.g., y = 2x and y = -1/2x + 1 are parallel because their slopes are reciprocals to each other, and the sign is flipped.

To know whether y = 4x + 3 and 4x + y = 3 are parallel, perpendicular, or neither, we have to identify the slopes and use what was mentioned previously:

Identifying the slope:

y = 4x + 3 slope = 4

4x + y = 3 --> y = -4x + 3 slope = -4

The slopes are different, so they are not parallel

As the slopes are not reciprocals, they are not perpendicular.

The graphs are neither parallel nor perpendicular.

User Adrian Wible
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