Question

which equation is represented by the graph?
options:

• $-3x - y = 6$
• $3x - y = 6$
• $-3x + y = 6$
• $3x + y = 6$

Explanation:

Step1: Identify intercepts from graph

The line crosses the x-axis at $x=-2$ (point $(-2,0)$) and y-axis at $y=-6$ (point $(0,-6)$).

Step2: Test points in equations

Test $(0,-6)$ in each option:

• For $-3x - y = 6$: $-3(0) - (-6) = 6$, $6=6$ (true)
• For $3x - y = 6$: $3(0) - (-6) = 6$, $6=6$ (true)
• For $-3x + y = 6$: $-3(0) + (-6) = -6

eq 6$ (false)

• For $3x + y = 6$: $3(0) + (-6) = -6

eq 6$ (false)

Now test $(-2,0)$ in remaining valid options:

• For $-3x - y = 6$: $-3(-2) - 0 = 6$, $6=6$ (true)
• For $3x - y = 6$: $3(-2) - 0 = -6

eq 6$ (false)

Answer:

$-3x - y = 6$