how to decide whether lines with the given equation are parallel, perpendicular,or neither

y=-5x-2
y=5x+2

parallel

To determine whether two lines with given equations are parallel, perpendicular, or neither, you need to examine the slopes of the lines.

1. Start by comparing the two equations and identifying the slope-intercept form: y = mx + b, where m represents the slope of the line.

For the first equation, y = -5x - 2, the slope is -5.
For the second equation, y = 5x + 2, the slope is 5.

2. Compare the slopes of the two lines:

- If the slopes are equal, the lines are parallel.
- If the product of the slopes is -1, the lines are perpendicular.
- If the slopes are neither equal nor the negative reciprocal of each other, the lines are neither parallel nor perpendicular.

Let's apply these steps to the given equations:

For y = -5x - 2, the slope is -5.
For y = 5x + 2, the slope is 5.

Since the slopes (-5 and 5) are negative reciprocals of each other (i.e., their product is -1), the lines represented by these equations are perpendicular.