Question

1. $g(x)=\frac{-x - 5}{3}$

Explanation:

Step1: Rewrite in slope-intercept form

$g(x) = -\frac{1}{3}x - \frac{5}{3}$

Step2: Identify y-intercept

The y-intercept is $b = -\frac{5}{3} \approx -1.67$, so plot the point $(0, -\frac{5}{3})$.

Step3: Identify slope

Slope $m = -\frac{1}{3}$, meaning for every 3 units right, move 1 unit down. From $(0, -\frac{5}{3})$, move 3 right to $x=3$, then 1 down to $y = -\frac{5}{3} - 1 = -\frac{8}{3} \approx -2.67$, giving the point $(3, -\frac{8}{3})$.

Step4: Draw the line

Connect the two points and extend the line across the grid.

Answer:

The graph is a straight line with slope $-\frac{1}{3}$ and y-intercept at $(0, -\frac{5}{3})$, passing through points like $(0, -\frac{5}{3})$ and $(3, -\frac{8}{3})$.