Answer:
The lines are perpendicular
Step-by-step explanation:
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 their slopes is equal to -1)
we have
[tex]3x+7y=15[/tex] ----> equation A
isolate the variable y
[tex]7y=-3x+15[/tex]
Divide by 7 both sides
[tex]y=-\frac{3}{7}x+\frac{15}{7}[/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
[tex]3y=7x-6[/tex]
Divide by 3 both sides
[tex]y=\frac{7}{3}x-2[/tex]
The slope of the line B is [tex]m_B=\frac{7}{3}[/tex]
Compare the slope of both lines
[tex]m_A=-\frac{3}{7}[/tex]
[tex]m_B=\frac{7}{3}[/tex]
so
[tex]m_A \neq m_B[/tex] ----> the lines are not parallel
Find the product of the slopes
[tex]-\frac{3}{7}(\frac{7}{3})=-1[/tex] ----> the lines are perpendicular
