Question

The lines represented by the equations 3, y, minus, 2, x, equals, minus, 183y−2x=−18 and y, minus, start fraction, 2, divided by, 3, end fraction, x, equals, minus, 9y− 3 2 ​ x=−9 are Answer Multiple Choice Answers perpendicular the same line neither parallel nor perpendicular parallel

Answer 1

The two lines provided in the equations are parallel because they have the same slope but different y-intercepts.

To determine the relationship between two lines, we have to compare their slopes. The slope of a line in the slope-intercept form (y = mx + b) is given by the coefficient 'm' of 'x'. The equations of the lines given are 3y - 2x = -18 and y - 2⁄3x = -9.

Let's first convert both equations to the slope-intercept form (y = mx + b).

For the first equation:

1. Multiply both sides by 1/3 to get y on its own: y = 2⁄3x + 6.

For the second equation:

1. It is already in slope-intercept form: y = 2⁄3x + 9.

Both lines have the same slope, slope of 2⁄3, but different y-intercepts. Therefore, they are parallel to each other.