Question

What is the relationship between the lines represented by the equations -6x - 3y = -4 and 2x - 8y = 9? Are these lines parallel, perpendicular, or neither?

Answer 1

The lines represented by the equations -6x - 3y = -4 and 2x - 8y = 9 are neither parallel nor perpendicular.

Step-by-step explanation:

The given equations are:

• -6x - 3y = -4
• 2x - 8y = 9

To determine the relationship between these lines, we can compare their slopes. The slope-intercept form of a linear equation is y = mx + b, where m is the slope. Let's rearrange the equations to be in slope-intercept form:

• -3y = 6x - 4 --> y = -2x + 4/3
• -8y = -2x + 9 --> y = 1/4x - 9/8

By comparing the two equations, we can see that the slopes are different (-2 and 1/4), which means the lines are not parallel. Moreover, the product of their slopes is (-2)(1/4) = -1/2, which is not -1, so the lines are also not perpendicular. Therefore, the lines represented by the given equations are neither parallel nor perpendicular.