# 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?

None of these

#### Explanation:

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

$y = f \left(x\right) = - 8 x$

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

$- y = - 8 x$

$y = 8 x$

$\setminus \ne f \left(x\right)$

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

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

$y = - 8 \left(- x\right)$

$y = 8 x$

$\setminus \ne f \left(x\right)$

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

$x = - 8 y$

$y = - \frac{1}{8} x$

$\setminus \ne f \left(x\right)$

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

$- x = - 8 \left(- y\right)$

$y = - \frac{1}{8} x$

$\setminus \ne f \left(x\right)$

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

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