Question

which of the following equations does the graph below represent?
answer
$\boldsymbol{-3x + y = 36}$
$\boldsymbol{2x - 3y = 36}$
$\boldsymbol{-3x + 2y = 36}$
$\boldsymbol{x + 2y = 36}$

Explanation:

Step1: Identify intercept points

The line crosses $x$-axis at $(-12, 0)$ and $y$-axis at $(0, 18)$.

Step2: Test $x$-intercept in options

Substitute $x=-12, y=0$ into each equation:

1. For $-3x + y = 36$: $\frac{-3(-12)+0=36}{36=36}$ (true)
2. For $-3x + 2y = 36$: $\frac{-3(-12)+2(0)=36}{36=36}$ (true)
3. For $2x - 3y = 36$: $\frac{2(-12)-3(0)=36}{-24

eq36}$ (false)

1. For $x + 2y = 36$: $\frac{-12+2(0)=36}{-12

eq36}$ (false)

Step3: Test $y$-intercept in remaining options

Substitute $x=0, y=18$ into remaining equations:

1. For $-3x + y = 36$: $\frac{-3(0)+18=36}{18

eq36}$ (false)

1. For $-3x + 2y = 36$: $\frac{-3(0)+2(18)=36}{36=36}$ (true)

Answer:

$-3x + 2y = 36$