Question 1-16 Given the equation x-3y=6 determine the slope of the line m=-3 m=3 m=-(1)/(3) m-(1)/(3)

To determine the slope of the line given by the equation $x - 3y = 6$, we need to rewrite the equation in slope-intercept form, which is $y = mx + b$, where $m$ is the slope.<br /><br />Starting with the given equation:<br />\[ x - 3y = 6 \]<br /><br />First, solve for $y$:<br />\[ -3y = x - 6 \]<br />\[ y = -\frac{1}{3}x + 2 \]<br /><br />Now, the equation is in the form $y = mx + b$, where $m$ is the slope. From the equation $y = -\frac{1}{3}x + 2$, we can see that the slope $m$ is $-\frac{1}{3}$.<br /><br />Therefore, the correct answer is:<br />\[ m = -\frac{1}{3} \]