Question

What is the graph of the inequality?
-3y ≥ 6x - 3

Answer 1

It appears you are offline, so I will provide a walkthrough that you can refer to, and if you need further help after you return you can try more specific questions or bumping this one!
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Our goal is to get y isolated with no coefficient. In this equation, we have \( \color{Red}{-3} y \ge 6x - 3 \). The red -3 is the culprit making this problem difficult. We should divide it off from both sides.

Because the value is negative, we have to flip the inequality sign in the process. Doing so and dividing off accordingly, we get:
\( \dfrac{\color{red}{-3}y}{\color{reD}{-3}} \color{magenta}\le \dfrac{6x - 3}{\color{red}{-3}} \)
The left side simplifies to y. The right side we distribute the denominator and accordingly divide each value.
\( y \color{magenta} \le -2x + 1 \)

Now... graph this equation as if it were just an equation. y = -2x + 1. We use a solid line because the inequality is less than OR EQUAL to; the poitns on the line are inclusive. Then, we could pick some value not on the line and test the inequality. (0, 0) is not on the line. \( 0 \le -2 * 0 + 1 \) seems to be true, so we can shade the entire region at the same side as (0,0) from the line y=-2x+1