Question

which of the following equations does the graph below represent?
answer
$4x + y = 12$
$-3x + 4y = 12$
$4x + 3y = 12$
$4x - 3y = 12$

Explanation:

Step1: Identify intercepts from graph

The line crosses the x-axis at $(3, 0)$ and y-axis at $(0, -4)$.

Step2: Test x-intercept on each option

For $(3,0)$:

• $4(3)+0=12 \implies 12=12$ (true for $4x+y=12$)
• $4(3)+3(0)=12 \implies 12=12$ (true for $4x+3y=12$)
• $-3(3)+4(0)=12 \implies -9

eq12$ (false)

• $4(3)-3(0)=12 \implies 12=12$ (true for $4x-3y=12$)

Step3: Test y-intercept on remaining options

For $(0,-4)$:

• $4(0)+(-4)=12 \implies -4

eq12$ (false)

• $4(0)+3(-4)=12 \implies -12

eq12$ (false)

• $4(0)-3(-4)=12 \implies 12=12$ (true)

Answer:

$4x - 3y = 12$