Question

which of the following equations does the graph below represent?
answer
$\boldsymbol{-3x - 6y = 36}$
$\boldsymbol{-3x + 6y = 36}$
$\boldsymbol{x + 6y = 36}$
$\boldsymbol{3x + 6y = 36}$

Explanation:

Step1: Identify intercepts from graph

x-intercept: $x=-12$ (when $y=0$); y-intercept: $y=6$ (when $x=0$)

Step2: Test intercepts in options

For $-3x + 6y = 36$:

• Substitute $x=-12, y=0$: $\ -3(-12) + 6(0) = 36 + 0 = 36$, which matches.
• Substitute $x=0, y=6$: $\ -3(0) + 6(6) = 0 + 36 = 36$, which matches.

Step3: Verify slope consistency

Rewrite to slope-intercept form:
$6y = 3x + 36$ → $y = \frac{1}{2}x + 6$. Slope $\frac{1}{2}$ matches the graph's positive, shallow slope.

Answer:

-3x + 6y = 36