Tell whether the lines for the pair of equations are parallel, perpendicular, or neither.
y = –two over threex + 1
2x – 3y = –3
(1 point)
Responses
parallel
perpendicular
neither
To determine whether the lines for the pair of equations are parallel, perpendicular, or neither, we can compare the slopes of the two lines.
The first equation is in slope-intercept form y = mx + b, where m is the slope. Here, the slope is -2/3.
The second equation is in standard form Ax + By = C. We need to rearrange it to slope-intercept form to find the slope.
2x - 3y = -3
-3y = -2x - 3
y = (2/3)x + 1
Comparing the slopes, we see that the slope of the first line is -2/3 and the slope of the second line is 2/3.
Since the slopes are negative reciprocals (multiplicative inverses) of each other, the lines are perpendicular. So the answer is: perpendicular.