Question

which equation represents the graph below?
options:
○ ( x + 2y = 4 )
○ ( 2x + 4y = 8 )
○ ( 2x + y = 4 )
○ ( -2x + 4y = 4 )

Explanation:

Step1: Find intercepts from graph

The line crosses y-axis at (0, 4) and x-axis at (2, 0) (since from graph, when x=2, y=0).

Step2: Test intercepts in equations

• For \(2x + y = 4\):
• At x=0, \(2(0)+y = 4\) ⇒ \(y = 4\) (matches y-intercept).
• At y=0, \(2x+0 = 4\) ⇒ \(x = 2\) (matches x-intercept).
• Check other options:
• \(x + 2y = 4\): At x=0, \(2y=4\) ⇒ y=2 (doesn't match y=4).
• \(2x + 4y = 8\): Simplify to \(x + 2y = 4\) (same as above, y-intercept 2, no).
• \(-2x + 4y = 4\): At x=0, \(4y=4\) ⇒ y=1 (no).

Answer:

\(2x + y = 4\) (the option with this equation, likely the third option as per the circle in the image)