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Determine if the equations are parallel, perpendicular, or neither.

5x + 3y = 3 and 3x + 5y = -25

User Muatik
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1 Answer

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Final answer:

After converting both equations to slope-intercept form, we find that the slopes are -5/3 and -3/5 respectively. Since the slopes are neither equal nor negative reciprocals of one another, the lines are neither parallel nor perpendicular.

Step-by-step explanation:

To determine if the equations 5x + 3y = 3 and 3x + 5y = -25 are parallel, perpendicular, or neither, we first need to write each equation in slope-intercept form, y = mx + b, where m represents the slope.

For the first equation, 5x + 3y = 3:

Subtract 5x from both sides: 3y = -5x + 3

Divide everything by 3: y = (-5/3)x + 1

The slope of the first line is -5/3.

For the second equation, 3x + 5y = -25:

Subtract 3x from both sides: 5y = -3x - 25

Divide everything by 5: y = (-3/5)x - 5

The slope of the second line is -3/5.

Two lines are parallel if they have the same slope and perpendicular if the product of their slopes is -1. In this case:

The slopes are not equal, so the lines are not parallel.

The product of the slopes is (-5/3) * (-3/5) = 1, which is not -1, so the lines are not perpendicular.

Therefore, the lines represented by the equations 5x + 3y = 3 and 3x + 5y = -25 are neither parallel nor perpendicular.

User JD Brennan
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