Question
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
2 y = -3x+1 2x-3y = -3
(1 point)
parallel
perpendicular
neither
Answers
GPT 3.5
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.
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.