Question

Are the two lines parallel, perpendicular, or neither? Explain your answer. Show work needed to answer the question.

Answer 1

For this case we have the following line equations:$3x + 7y = 15\\7x-3y = 6$

We manipulate the equations algebraically until we write them in the slope-intersection form,$y = mx + b:$

Equation 1:

$3x + 7y = 15\\7y = -3x + 15\\y = - \frac {3} {7} x + \frac {15} {7}$

Equation 2:

$7x-3y = 6\\-3y = -7x + 6\\y = \frac {-7} {- 3} x + \frac {6} {- 3}\\y = \frac {7} {3} x-2$

By definition we have:

If two lines are parallel then their slopes are equal.

If two lines are perpendicular then the product of their slopes is -1.

It is noted that the slopes are not equal. We check if the product is -1:

$- \frac {3} {7} * \frac {7} {3} = - \frac {3 * 7} {7 * 3} = \frac {-21} {21} = - 1$

Thus, the lines are perpendicular.

Answer:

The lines are perpendicular