Questions: -6y-12 ≤ 2x

Solution Steps

To identify two points from the line represented by the inequality \(-6y - 12 \leq 2x\), we can first convert the inequality into an equation by replacing the inequality sign with an equal sign. Then, we can solve for \(y\) in terms of \(x\) to get the equation of the line in slope-intercept form. Finally, we can choose two different values for \(x\) to find the corresponding \(y\) values, which will give us two points on the line.

We start with the inequality

\[ -6y - 12 \leq 2x \]

To find points on the line, we convert this inequality into an equation:

\[ -6y - 12 = 2x \]

Next, we solve for \(y\) in terms of \(x\):

\[ -6y = 2x + 12 \]

Dividing both sides by \(-6\) gives:

\[ y = -\frac{1}{3}x - 2 \]

We will now choose two values for \(x\) to find the corresponding \(y\) values. Let \(x = 0\) and \(x = 2\):

1. For \(x = 0\):

\[ y = -\frac{1}{3}(0) - 2 = -2 \]

Thus, the first point is \((0, -2)\).

2. For \(x = 2\):

\[ y = -\frac{1}{3}(2) - 2 = -\frac{2}{3} - 2 = -\frac{2}{3} - \frac{6}{3} = -\frac{8}{3} \]

Thus, the second point is \((2, -\frac{8}{3})\).

Final Answer