2x + 3y =6

2x + 3y = 4

I get these lines are neither parallel or perpendicular. Am I doing this right?

you have to change the equation

3y=-2x-4 -divide it by 3 to leave the y alone and you get:
y=-2/3x-4/3

3y=-2x-6 again, divide by 3
y=-2x/3-2

They have the same slopes: 2/3x

So they would be Parallel correct?

Thank you

yess

yupp...do you get it?

Yes, you are correct. The equations 2x + 3y = 6 and 2x + 3y = 4 represent two lines. To determine if they are parallel or perpendicular, we can compare their slopes.

The given equations can be rewritten in slope-intercept form (y = mx + b) by isolating y:

2x + 3y = 6
3y = -2x + 6
y = (-2/3)x + 2

2x + 3y = 4
3y = -2x + 4
y = (-2/3)x + 4/3

By comparing the slopes of the two lines, which are represented by the coefficients of x (-2/3) in both cases, we can conclude that the slopes are equal. This means the lines are not perpendicular.

However, since the y-intercepts are different (2 and 4/3), the lines are also not parallel. Therefore, your conclusion is correct: the given lines are neither parallel nor perpendicular to each other.