Question

Choose all the lines that would be parallel to the line -2x + 3y = 12. Select two correct answers.

Options:
a) y = (2/3)x - 1
b) -2x + y = 12
c) 3x - 2y = -2
d) 3x + 2y = 11

Answer 1

Option a) y = (2/3)x - 1 is parallel to the line -2x + 3y = 12 because it has the same slope of 2/3. The other options do not have the same slope and therefore are not parallel.

Step-by-step explanation:

To determine which lines would be parallel to the given line -2x + 3y = 12, we first need to express this line in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Rewriting the equation, we have 3y = 2x + 12 or y = (2/3)x + 4, which reveals that the slope of the given line is 2/3.

Looking at the options provided:

• Option a) y = (2/3)x - 1 has the same slope, which means it is parallel to the given line.
• Options b), c), and d) do not have a slope of 2/3 and therefore are not parallel to the given line.

Thus, the lines that would be parallel to the line -2x + 3y = 12 are like option a) y = (2/3)x - 1, as it is the only one with a matching slope.