determine if the following lines are parallel, perpendicular or neither. Explain your reasoning.
-2x+3y=3 2x+3y=3
Rewrite them in y = mx + b form to get the slopes, m.
The lines are parallel of the slopes are the same. They are perpendicular if the product of the slopes is -1
I FOUND THAT Y=2X/3+1 AND Y=-2X/3+1
ARE THEY PERPENDICULAR, RIGHT???????
No, they aren't . The product of the slopes is not -1. It is -4/9 in this case
SO WHAT IS IT???????????????????????
Neither.
The given lines -2x+3y=3 and 2x+3y=3 can be rewritten in the form y = mx + b to determine their slopes.
For the first equation:
-2x+3y=3
Rearranging, we get:
3y = 2x + 3
Dividing by 3, we obtain:
y = (2/3)x + 1
For the second equation:
2x+3y=3
Rearranging, we get:
3y = -2x + 3
Dividing by 3, we obtain:
y = (-2/3)x + 1
Comparing the equations, we find that the slopes of both lines are (2/3) and (-2/3) respectively.
To determine if the lines are parallel or perpendicular, we need to check if the slopes are equal or if their product is -1.
In this case, the slopes are not equal, as 2/3 is not equal to -2/3. Additionally, their product is not -1. The product of (2/3) and (-2/3) is (-4/9).
Therefore, the given lines are neither parallel nor perpendicular to each other.