A line passes through the origin, and is parallel to the line \( 3 y=-x+23 \). Write down its equation.

To find the equation of a line that passes through the origin and is parallel to the line given by the equation \( 3y = -x + 23 \), we first need to determine the slope of the given line. 1. **Rearranging the equation**: We can rewrite the equation in slope-intercept form \( y = mx + b \), where \( m \) is the slope. Starting with: \[ 3y = -x + 23 \] we divide both sides by 3: \[ y = -\frac{1}{3}x + \frac{23}{3} \] From this, we see that the slope \( m \) of the line is \( -\frac{1}{3} \). 2. **Finding the equation of the parallel line**: Since parallel lines have the same slope, the line we are looking for will also have a slope of \( -\frac{1}{3} \). The general form of a line passing through the origin (0, 0) is: \[ y = mx \] Substituting the slope we found: \[ y = -\frac{1}{3}x \] Thus, the equation of the line that passes through the origin and is parallel to the line \( 3y = -x + 23 \) is: \[ \boxed{y = -\frac{1}{3}x} \]