How do you determine whether the graph of #y=-8x# is symmetric with respect to the x axis, y axis, the line y=x or y=-x, or none of these?

1 Answer

Answer:

None of these

Explanation:

The graph of given straight line: #y=-8x#

#y=f(x)=-8x#

1) Setting #y=-y# in given equation of line, we get

#-y=-8x#

#y=8x#

#\ne f(x)#

Hence, the graph of given function is not symmetrical about x-axis

2) Setting #x=-x# in given equation of line, we get

#y=-8(-x)#

#y=8x#

#\ne f(x)#

Hence, the graph of given function is not symmetrical about y-axis

3) Setting #y=x# & #x=y# in given equation of line, we get

#x=-8y#

#y=-1/8x#

#\ne f(x)#

Hence, the graph of given function is not symmetrical about #y=x#

4) Setting #y=-x# & #x=-y# in given equation of line, we get

#-x=-8(-y)#

#y=-1/8x#

#\ne f(x)#

Hence, the graph of given function is not symmetrical about #y=-x#

hence graph of given line is symmetrical about none of given options