Question

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

Answer 1

Answer:

The lines are perpendicular

Step-by-step explanation:

The correct question is

Are the two lines parallel, perpendicular, or neither? Explain your answer

3x + 7y = 15

7x − 3y = 6

we know that

If two lines are parallel, then their slopes are equal

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

Remember that

The equation of the line in slope intercept form is equal to

$y=mx+b$

where m is the slope

b is the y-intercept

we have

$3x + 7y = 15$ ----> equation A

isolate the variable y and convert the equation in slope intercept form

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

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

The slope of the line A is $m_A=-\frac{3}{7}$

$7x-3y = 6$ ---> equation B

isolate the variable y and convert the equation in slope intercept form

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

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

The slope of the line B is $m_B=\frac{7}{3}$

Compare the slopes

$m_A\neq m_B$ ---> the lines are not parallel

$m_A* m_B=(-\frac{3}{7})*(\frac{7}{3})=-1$

so

The slopes are opposite reciprocal

therefore

The lines are perpendicular