tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
2x-5y=0 and y+3=5/2x
To determine the relationship between the lines defined by the pair of equations, we need to find the slopes of each line.
The first equation, 2x - 5y = 0, can be rearranged to the form y = (2/5)x.
Comparing this equation to y + 3 = (5/2)x, we can see that the second equation is already in slope-intercept form, y = (5/2)x - 3.
The slopes of the lines are therefore 2/5 and 5/2, respectively.
If two lines are parallel, their slopes must be equal. However, 2/5 and 5/2 are not equal. Therefore, the lines defined by the pair of equations are not parallel.
If two lines are perpendicular, the product of their slopes must be -1. However, (2/5) * (5/2) = 1, not -1. Therefore, the lines defined by the pair of equations are not perpendicular.
Since the slopes are neither equal nor the negative reciprocal of each other, we can determine that the lines defined by the pair of equations are neither parallel nor perpendicular, but are simply two intersecting lines.