Find the Linear Equation: Line Negative When x < -2

A line is negative in the domain

$x < -2$.

Which equation represents the line?

To determine which equation represents a line that is negative for $x < -2$, we will evaluate each option by substituting $x = -3$, which is less than -2:

• For $y = 7x + 14$: Substituting $x = -3$, we have $y = 7(-3) + 14 = -21 + 14 = -7$. This is negative, satisfying the condition.
• For $y = 3x + 6$: Substituting $x = -3$, we have $y = 3(-3) + 6 = -9 + 6 = -3$. This is also negative, meeting the requirement.
• For $y = 1\frac{1}{2}x + 3$: Substituting $x = -3$, we have $y = 1.5(-3) + 3 = -4.5 + 3 = -1.5$. Again, the result is negative.

All equations give negative values for $x < -2$. Therefore, any of them represent a line that satisfies the given condition.

Hence, all answers are correct.