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poizon [28]
2 years ago
11

Two basketballs are thrown along different paths. Determine if the basketballs’ paths are parallel to each

Mathematics
1 answer:
Paul [167]2 years ago
3 0

Answer:

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

Step-by-step explanation:

Remember that:

  • Two lines are parallel if their slopes are equivalent.
  • Two lines are perpendicular if their slopes are negative reciprocals of each other.
  • And two lines are neither if neither of the two cases above apply.

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

The first basketball is modeled by:

\displaystyle 3x+4y=12

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

4y=-3x+12

And divide both sides by four:

\displaystyle y=-\frac{3}{4}x+3

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

The second basketball is modeled by:

-6x-8y=24

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

-8y=6x+24

And divide both sides by negative eight:

\displaystyle y=-\frac{3}{4}x-3

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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