Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?

Answers + Explanation:

1. Red inequality

First, find the equation of the red line.

You can see that when x goes up by 2, y goes down by 3 so the slope would be -3/2 or -1/5.

Then, the y-intercept is 1.5 so the equation is y = -1.5x + 1.5.

Since you can see the green part is below the red line and the line is solid, the inequality would have a ≤ sign.

The inequality is y ≤ -1.5x + 1.5

2. Blue inequality

Next, find the equation of the blue line.

You can see that when x goes up by 4, y goes down by 3 so the slope of the line would be -3/4 or -0.75.

Next, you can see that the y-intercept is 0.5.

This means that the equation of the line is y = -0.75x + 0.5.

Since the green shaded part is above the blue line and the blue line is solid, the inequality will have a ≥ sign.

It would be y ≥ -0.75x + 0.5

3. Test point

Any point in the green shaded section should work as a test point. For example, you can use (-1, 2)

Plug this into both in equalities:

Red: 2 ≤ -1.5 * -1 + 1.5

2 ≤ 1.5 + 1.5

2 ≤ 3

true

Blue: 2 ≥ -0.75 * -1 + 0.5

2 ≥ 0.75 + 0.5

2 ≥  1.25

true

Both are true so this is correct.

water molecules will move from the side of higher water concentration to the side of lower concentration until both solutions are isotonic. at this point, equilibrium is reached. in an isotonic solution, the flow of water in and out of the cell is happening at the same rate.

hope this < 3

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