1. The problem is to analyze the function $g(x) = 8 - 3x$ and understand its properties. 2. This is a linear function of the form $g(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Here, the slope $m = -3$ and the y-intercept $b = 8$. 4. The slope $-3$ means the line descends from left to right, decreasing by 3 units in $g(x)$ for every 1 unit increase in $x$. 5. To find the x-intercept, set $g(x) = 0$: $$0 = 8 - 3x$$ $$3x = 8$$ $$x = \frac{8}{3}$$ 6. The y-intercept is the value of $g(x)$ when $x=0$, which is $8$. 7. The graph is a straight line crossing the y-axis at $(0,8)$ and the x-axis at $(\frac{8}{3},0)$, descending with slope $-3$. Final answer: The function $g(x) = 8 - 3x$ is a line with slope $-3$, y-intercept $8$, and x-intercept $\frac{8}{3}$.