Question

Tell whether the lines for the pair of equations are parallel, perpendicular, or neither.

y = negative two-thirdsx + 1
2x – 3y = –3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine whether two lines are parallel, perpendicular, or neither, we need to compare the slopes of the lines.

For the first equation, y = -2/3x + 1, we can see that the slope is -2/3.

To determine the slope of the second equation, we need to rewrite it in slope-intercept form (y = mx + b), where m is the slope.
2x - 3y = -3
-3y = -2x - 3
y = 2/3x + 1

From the second equation, it is clear that the slope is 2/3.

Comparing the slopes of both lines, we see that the slopes are negative reciprocals of each other. -2/3 and 2/3 are negative reciprocals because if we take the product of the slopes, we get (-2/3) * (2/3) = -4/9.

Since the slopes are negative reciprocals, the lines are perpendicular to each other.