Tell whether the lines for the pair of equations are parallel, perpendicular, or neither.
2 y = -3x+1 2x-3y = -3
(1 point)
parallel
perpendicular
neither
To determine if the lines are parallel, perpendicular, or neither, we need to compare the slopes of the two lines.
Rewrite the given equations in slope-intercept form (y = mx + b):
For the first equation, 2y = -3x + 1, divide both sides by 2: y = (-3/2)x + 1/2.
The slope of the first line is -3/2.
For the second equation, 2x - 3y = -3, rewrite it in slope-intercept form: -3y = -2x - 3, divide both sides by -3: y = (2/3)x + 1.
The slope of the second line is 2/3.
Since the slopes of the two lines, -3/2 and 2/3, are not equal to each other and their product is not -1 (which would make them perpendicular), we can conclude that the lines are neither parallel nor perpendicular.