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
[tex]y=mx+b[/tex]
where m is the slope
b is the y-intercept
we have
[tex]3x + 7y = 15[/tex] ----> equation A
isolate the variable y and convert the equation in slope intercept form
[tex]y=\frac{15-3x}{7}[/tex]
[tex]y=\frac{15}{7}-\frac{3}{7}x[/tex]
The slope of the line A is [tex]m_A=-\frac{3}{7}[/tex]
[tex]7x-3y = 6[/tex] ---> equation B
isolate the variable y and convert the equation in slope intercept form
[tex]y=\frac{7x-6}{3}[/tex]
[tex]y=\frac{7}{3}x-2[/tex]
The slope of the line B is [tex]m_B=\frac{7}{3}[/tex]
Compare the slopes
[tex]m_A\neq m_B[/tex] ---> the lines are not parallel
[tex]m_A* m_B=(-\frac{3}{7})*(\frac{7}{3})=-1[/tex]
so
The slopes are opposite reciprocal
therefore
The lines are perpendicular
