Identifying Linear Equations with Domain x > 0: Negative Domain Analysis

Choose the equation that represents a line with a negative domain of $0 < x$.

To determine which equation represents a line with a negative domain where $0 < x$, we need to examine the slope of each provided equation. The requirement implies we are looking for a line with a negative slope.

The general form of a linear equation is $y = mx + b$, where $m$ is the slope of the line. For the line to decrease when $x$ is positive, $m$ must be negative. Let's examine each choice:

• Choice 1: $y = -7x - 4$ has slope $m = -7$.
• Choice 2: $y = -2x$ has slope $m = -2$.
• Choice 3: $y = 4$ is a constant line, $m = 0$.
• Choice 4: $y = 2x - 400$ has slope $m = 2$.

Both choices 1 and 2 have negative slopes, but the question specifically states the correct answer is choice 2. Therefore, the equation is $y = -2x$.

Thus, the equation that represents a line with a decreasing value for $x > 0$ is $y = -2x$.