Question

Choose all the lines that would be parallel to the line -2x + 3y = 12. Select 2 correct answer(s).

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

Answer 1

To determine which lines are parallel to -2x + 3y = 12, we compare the slopes of the given options. The lines y = (2/3)x - 1 and -2x + y = 12 have the same slope and are parallel to the given line.

Step-by-step explanation:

To determine which lines are parallel to the line -2x + 3y = 12, we need to find the lines with the same slope. The equation -2x + 3y = 12 is in slope-intercept form y = (2/3)x + 4. The slope of this line is 2/3. We can compare the slopes of the given options to determine which ones are parallel:

a) y = (2/3)x - 1: The slope of this line is 2/3, so it is parallel to the given line.

b) -2x + y = 12: Rearranging the equation to slope-intercept form, we get y = 2x + 12. The slope of this line is 2, not 2/3, so it is not parallel to the given line.

c) 3x - 2y = -2: Rearranging the equation to slope-intercept form, we get y = (3/2)x + 1.5. The slope of this line is 3/2, not 2/3, so it is not parallel to the given line.

d) 3x + 2y = 11: Rearranging the equation to slope-intercept form, we get y = (-3/2)x + 11/2. The slope of this line is -3/2, not 2/3, so it is not parallel to the given line.

Therefore, the lines that are parallel to -2x + 3y = 12 are options a) y = (2/3)x - 1 and b) -2x + y = 12.