Question

which of the following equations does the graph below represent?
answer
$2x - 10y = 20$
$-2x - 10y = 20$
$2x + 10y = 20$
$-10x + 2y = 20$

Explanation:

Step1: Find x-intercept (y=0)

The graph crosses x-axis at $(10, 0)$. Substitute $y=0$ into each option:

• For $2x - 10y = 20$: $2x=20 \implies x=10$ (matches)
• For $2x + 10y = 20$: $2x=20 \implies x=10$ (matches)
• For $-2x - 10y = 20$: $-2x=20 \implies x=-10$ (does not match)
• For $-10x + 2y = 20$: $-10x=20 \implies x=-2$ (does not match)

Step2: Find y-intercept (x=0)

The graph crosses y-axis at $(0, -2)$. Substitute $x=0$ into remaining options:

• For $2x - 10y = 20$: $-10y=20 \implies y=-2$ (matches)
• For $2x + 10y = 20$: $10y=20 \implies y=2$ (does not match)

Step3: Verify slope consistency

Rewrite $2x - 10y = 20$ to slope-intercept form $y=mx+b$:
$-10y = -2x + 20 \implies y=\frac{2}{10}x - 2 = \frac{1}{5}x - 2$
The graph has a positive slope $\frac{1}{5}$, which matches.

Answer:

$2x - 10y = 20$