Question

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?

Answer 1

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