Question 1: Which inequality is shown on the graph?

To determine the inequality, we need to consider two aspects:

1. Slope of the line: The slope ($m$) can be identified based on how steep the line is. The given options have slopes like $-4$, $-\frac{1}{4}$, and $4$, so the graph must show whether it's steep or relatively flat.

2. Y-intercept: This is the point where the line crosses the y-axis. It's given in the options as $+5$ in some of the choices.

The line must also show whether the inequality uses a strict inequality ("<" or ">") or includes the boundary ("≤" or "≥"). If the line is dashed, it represents strict inequalities ("<" or ">"). If the line is solid, it represents inclusive inequalities ("≤" or "≥").

Assuming you are asking about a specific inequality related to this graph:

• If the line has a negative slope and crosses the y-axis at +5, then the inequality might look like $y < -4x + 5$ or $y < -\frac{1}{4}x + 5$.

• If the shading is below the line, the inequality would use "<" (less than). If the shading is above the line, the inequality would use ">".

Given the choices, Option C $y < -4x + 5$ seems likely if the line has a negative slope and crosses the y-axis at 5, with shading below the line.

Question 2: Which ordered pair is NOT a solution to the inequality?

For this, plug in the given ordered pairs into the inequality from Question 1, assuming the inequality is $y < -4x + 5$.

Checking the pairs:

1. (1, 1): $y = 1 \quad \text{and} \quad x = 1$ Plug into $y < -4x + 5$: $1 < -4(1) + 5 \quad \Rightarrow \quad 1 < -4 + 5 \quad \Rightarrow \quad 1 < 1 \quad (\text{False} \ because \ 1 \not< 1)$ So, (1, 1) is NOT a solution.

2. (0, 2): $y = 2 \quad \text{and} \quad x = 0$ Plug into $y < -4x + 5$: $2 < -4(0) + 5 \quad \Rightarrow \quad 2 < 5 \quad (\text{True})$ So, (0, 2) is a solution.

3. (1, -2): $y = -2 \quad \text{and} \quad x = 1$ Plug into $y < -4x + 5$: $-2 < -4(1) + 5 \quad \Rightarrow \quad -2 < -4 + 5 \quad \Rightarrow \quad -2 < 1 \quad (\text{True})$ So, (1, -2) is a solution.

4. (-2, -2): $y = -2 \quad \text{and} \quad x = -2$ Plug into $y < -4x + 5$: $-2 < -4(-2) + 5 \quad \Rightarrow \quad -2 < 8 + 5 \quad \Rightarrow \quad -2 < 13 \quad (\text{True})$ So, (-2, -2) is a solution.

Thus, the ordered pair (1, 1) is NOT a solution, and the correct answer for Question 2 is A.

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Relative Questions:

1. How do you determine the slope of a line from a graph?
2. How does shading on a graph help identify the inequality?
3. What is the significance of the y-intercept in linear equations?
4. Why are dashed lines used for strict inequalities?
5. How can we verify if an ordered pair is a solution to a given inequality?

Tip:

Always check the direction of shading on the graph to identify whether the inequality uses "<" (shading below the line) or ">" (shading above the line).