Are these two lines parallel, perpendicular, or neither? Explain.

#9x+3y=8#,
#3x+9y=8#

Question

Are these two lines parallel, perpendicular, or neither? Explain.

#9x+3y=8#,
#3x+9y=8#

Claire Akin · Accepted Answer

The given lines are neither parallel nor perpendicular.

To check if two lines are parallel or perpendicular it is good to change the equations to form #y=ax+b# The first line is: #9x+3y=8# #3y=-9x+8# #y=-3x+8/3# The second line is: #3x+9y=8# #9y=-3x+8# #y=-1/3x+8/9# From those equations we can see that those lines are neither parallel nor perpendicular They would be parallel if the coefficients of #x# were equal. They would be perpendicular if the coefficients of #x# were inverse and opposite numbers (for example #3# and #(-1/3)# or #(-2)# and #1/2#)

Evelyn Arboleda · Answer

undefined To determine if two lines are parallel, perpendicular, or neither, we examine their slopes. We first rewrite the equations in slope-intercept form (y = mx + b), where m represents the slope:

For the first equation, 9x + 3y = 8:
$$3y = -9x + 8$$
$$y = -3x + \frac{8}{3}$$

For the second equation, 3x + 9y = 8:
$$9y = -3x + 8$$
$$y = -\frac{1}{3}x + \frac{8}{9}$$

Comparing the slopes of the two lines:

The slope of the first line is -3.
The slope of the second line is -1/3.

Since the product of the slopes is not -1, the lines are not perpendicular. Since the slopes are not equal, the lines are not parallel. Therefore, these lines are neither parallel nor perpendicular.

Are these two lines parallel, perpendicular, or neither? Explain. #9x+3y=8#, #3x+9y=8#