Question

which of the following equations does the graph below represent?
answer
$3x + 6y = 12$
$-3x + 6y = 12$
$3x - 6y = 12$
$x + 6y = 12$

Explanation:

Step1: Identify intercept points

The line crosses the y-axis at $(0, 2)$ and the x-axis at $(4, 0)$.

Step2: Test y-intercept in options

Substitute $x=0, y=2$ into each equation:

• For $3x + 6y = 12$: $3(0)+6(2)=12$, $12=12$ (valid)
• For $-3x + 6y = 12$: $-3(0)+6(2)=12$, $12=12$ (valid)
• For $3x - 6y = 12$: $3(0)-6(2)=-12

eq12$ (invalid)

• For $x + 6y = 12$: $0+6(2)=12$, $12=12$ (valid)

Step3: Test x-intercept in remaining options

Substitute $x=4, y=0$ into valid equations:

• For $3x + 6y = 12$: $3(4)+6(0)=12$, $12=12$ (valid)
• For $-3x + 6y = 12$: $-3(4)+6(0)=-12

eq12$ (invalid)

• For $x + 6y = 12$: $4+6(0)=4

eq12$ (invalid)

Answer:

$3x + 6y = 12$