Question

which of the following equations does the graph below represent?
answer
$x - 3y = 12$
$-3x + 3y = 12$
$3x + y = 12$
$3x - 3y = 12$

Explanation:

Step1: Identify intercepts

The line crosses the x-axis at $(4, 0)$ and y-axis at $(0, -4)$.

Step2: Test x-intercept in options

Substitute $x=4, y=0$ into each equation:

• $x-3y=12$: $4-0=4

eq12$

• $-3x+3y=12$: $-12+0=-12

eq12$

• $3x+y=12$: $12+0=12$, but check y-intercept next
• $3x-3y=12$: $12-0=12$, check y-intercept next

Step3: Test y-intercept in valid options

Substitute $x=0, y=-4$:

• $3x+y=12$: $0+(-4)=-4

eq12$

• $3x-3y=12$: $0-3(-4)=12$, which matches

Step4: Verify slope (optional)

Rearrange $3x-3y=12$ to slope-intercept form:
$y=x-4$, slope $m=1$, which matches the graph's slope $\frac{0-(-4)}{4-0}=1$.

Answer:

$3x - 3y = 12$