Answer
There is no axis or origin symmetry.
y-intercept: $(0,1)$
x-intercept: $(1/3,0)$
Graph:
Work Step by Step
(a) To test for x-axis symmetry, replace $y$ with $-y$
(b) To test for y-axis symmetry, replace $x$ with $-x$
(c) To test for origin symmetry, replace x with $-x$ and y with $-y$
and see if you obtain the same equation.
(a)
$-y=-3x+1$ ... is not the same equation.
(b)
$y=-3(-x)+1$
$y=3x+1$ ... is not the same equation.
(c)
$-y=-3(-x)+1$
$-y=3x+1$
$y=-3x-1 $ ... is not the same equation.
There is no axis or origin symmetry.
Intercepts: $\left[\begin{array}{ll}
\text{y-intercept} & \text{x-intercept}\\
x=0 & y=0\\
y=-0+1 & 0=-3x+1\\
y=1 & 3x=1\\
(0,1) & x=1/3\\
& (1/3,0)
\end{array}\right]$
Plot the intercepts and draw a line through them.
