Tell whether the lines for the pair of equations are parallel, perpendicular, or neither.
Y = -2/3x+1
2x-3y=-3
To determine whether the lines for the pair of equations are parallel, perpendicular, or neither, we need to compare their slopes.
First, let's rearrange the second equation to slope-intercept form (y = mx + b):
2x - 3y = -3
-3y = -2x - 3
y = (2/3)x + 1
Now we can compare the slopes of the two equations:
The slope of the first equation (Y = -2/3x + 1) is -2/3.
The slope of the second equation (y = 2/3x + 1) is 2/3.
Since the slopes are negative reciprocals of each other (i.e., (-2/3) * (2/3) = -4/9), the lines are perpendicular.