Two basketballs are thrown along different paths. Determine if the basketballs’ paths are parallel to each other, perpendicular or neither. Explain your reasoning.

o The first basketball is along the path 3x + 4y = 12
o The second basketball is along the path -6x – 8y = 24

Since the slopes of the two equations are equivalent, the basketballs' paths are parallel.

Step-by-step explanation:

Remember that:

So, let's find the slope of each equation.

The first basketball is modeled by:

We can convert this into slope-intercept form. Subtract 3x from both sides:

And divide both sides by four:

So, the slope of the first basketball is -3/4.

The second basketball is modeled by:

Again, let's convert this into slope-intercept form. Add 6x to both sides:

And divide both sides by negative eight:

So, the slope of the second basketball is also -3/4.

Since the slopes of the two equations are equivalent, the basketballs' paths are parallel.

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