Graphing Linear Inequalities Notes | Algebra 1 | TEKS A.2H - Classful - Free Printable

Let’s work through this step by step.

We’re looking at a set of “Scaffolded Notes” for graphing linear inequalities. The goal is to understand how to use the calculator notes and fill in the blanks based on inequality symbols.

Looking at the left-hand sheet titled “GRAPHING LINEAR INEQUALITIES”, we see four lines that start with:

- y > means that the line is ______ and shaded ______
- y ≥ means that the line is ______ and shaded ______
- y < means that the line is ______ and shaded ______
- y ≤ means that the line is ______ and shaded ______

Then below that, there’s a table called “CALCULATOR NOTES” with two columns: “DOTTED LINE” and “SOLID LINE”.

Under “DOTTED LINE”, it lists:
>
<

And under “SOLID LINE”, it lists:
≥
≤

Then it says:
SHADE ABOVE → CALC: ▼ (down arrow)
SHADE BELOW → CALC: ▲ (up arrow) — wait, actually looking again, it shows:

Actually, let me re-read carefully from the image description:

In the “CALCULATOR NOTES” box:

Left column (DOTTED LINE):
>
<

Right column (SOLID LINE):
≥
≤

Then below that:

“SHADE ABOVE” → CALC: ▼ (down arrow? That seems backwards — but let’s think logically.)

Wait — actually, in most graphing calculators, when you enter an inequality like y > mx + b, you choose whether to shade above or below. But here, they’re giving us a key:

It says:

For SHADE ABOVE → use CALC: ▼ (which might mean “select the option that shades above”)

But actually, looking at standard TI calculator behavior:

When you go to Y= and enter an inequality, you can press ENTER on the equals sign to cycle through options: usually, a triangle pointing up means “shade above”, and pointing down means “shade below”.

Wait — let’s clarify using logic.

If we have y > something, we want all points where y is greater — so that’s ABOVE the line.

Similarly, y < something → BELOW the line.

Now, for the calculator part:

The note says:

SHADE ABOVE → CALC: ▼
SHADE BELOW → CALC: ▲

That seems counterintuitive — because typically, an upward-pointing triangle means “shade above”. But maybe in their system, it’s reversed? Or perhaps it’s a typo? Let’s check the context.

Actually, looking back at the original problem — the user didn’t ask a specific question. They just uploaded an image of scaffolded notes.

But since the instruction says “Solve the problem accurately”, and the image contains blank spaces to fill in, I believe the task is to complete those blanks based on standard rules for graphing linear inequalities.

So let’s fill in the first part:

1. y > means that the line is dotted and shaded above

Why dotted? Because strict inequality (> or <) doesn’t include the line itself — so we draw a dashed/dotted line.

Shaded above? Yes — because y is greater than the expression, so we shade the region above the line.

2. y ≥ means that the line is solid and shaded above

Solid because it includes equality (≥), so the line is part of the solution.

Still shaded above — same reason as above.

3. y < means that the line is dotted and shaded below

Dotted because strict inequality.

Below because y is less than the expression.

4. y ≤ means that the line is solid and shaded below

Solid because includes equality.

Below because y is less than or equal.

Now, for the Calculator Notes section:

They already filled in:

DOTTED LINE: > , <
SOLID LINE: ≥ , ≤

That matches what we said.

Then:

SHADE ABOVE → CALC: ▼
SHADE BELOW → CALC: ▲

This might be referring to the icon you select on the calculator. On many TI calculators, when you’re in the Y= screen and you highlight the = sign next to your equation, pressing ENTER cycles through different graph styles:

- A normal line (for equations)
- An upward-pointing triangle (▲) which means “shade above”
- A downward-pointing triangle (▼) which means “shade below”

Wait — that contradicts what’s written here.

According to standard TI-84 behavior:

- ▲ (upward triangle) = shade ABOVE the line
- ▼ (downward triangle) = shade BELOW the line

But in the image, it says:

SHADE ABOVE → CALC: ▼
SHADE BELOW → CALC: ▲

That would be incorrect if following standard calculator icons.

Unless... perhaps it's a mistake in the worksheet? Or maybe it's referring to something else?

Alternatively, maybe “CALC: ▼” means “press the down arrow to get to the shading option”? That doesn't make sense.

Another possibility: perhaps “CALC: ▼” is meant to indicate the direction you move the cursor to select the correct shading style — but that seems unlikely.

Given that this is a student worksheet, and the rest of the content is standard, I suspect there might be a mix-up in the calculator notation.

But since the worksheet explicitly states:

SHADE ABOVE → CALC: ▼
SHADE BELOW → CALC: ▲

—we should probably go with what’s written, even if it contradicts standard calculator behavior, unless instructed otherwise.

However, for accuracy, let’s double-check with reliable sources.

Upon quick mental recall: In TI-84 Plus CE, when you are in the Y= editor, and you press ENTER on the = sign, you get options:

- \ (normal line)
- / (another line style)
- ▲ (shade above)
- ▼ (shade below)
- etc.

Yes — ▲ means shade above, ▼ means shade below.

Therefore, the worksheet has it backwards.

But since the user hasn’t asked a specific question, and we’re supposed to “solve the problem”, perhaps the problem is to identify errors or complete the blanks correctly.

Looking again at the image description — the left sheet has blanks to fill in for the four inequalities, and then the calculator notes are partially filled.

Perhaps the task is to complete the entire left sheet correctly.

So let’s do that.

Final completed version of the left sheet:

GRAPHING LINEAR INEQUALITIES

y > means that the line is dotted and shaded above

y ≥ means that the line is solid and shaded above

y < means that the line is dotted and shaded below

y ≤ means that the line is solid and shaded below

CALCULATOR NOTES

DOTTED LINE | SOLID LINE
---|---
> | ≥
< | ≤

SHADE ABOVE → CALC: ▲ *(correcting the worksheet)*
SHADE BELOW → CALC: ▼ *(correcting the worksheet)*

But since the worksheet says the opposite, and we don’t know if it’s intentional, perhaps we should note the discrepancy.

However, for the purpose of this exercise, since no specific question was asked, and the instruction is to “solve the problem accurately”, I will assume the problem is to provide the correct completions for the blanks in the worksheet.

Thus, the answers to fill in are:

First blank set:

1. dotted, above
2. solid, above
3. dotted, below
4. solid, below

Calculator notes: The shading indicators should be swapped for accuracy, but if we must follow the worksheet as-is, we leave them — but that would be teaching incorrectly.

Given that this is educational material, I think it’s important to correct it.

But the user didn’t specify what exactly to solve. Perhaps the “problem” is implied to be completing the notes.

Since the right side of the image shows example graphs, but no specific questions, I’ll focus on the left sheet.

To summarize, the correct completions are as above.

Final Answer:
For the blanks in "GRAPHING LINEAR INEQUALITIES":
- y > : dotted, above
- y ≥ : solid, above
- y < : dotted, below
- y ≤ : solid, below

For "CALCULATOR NOTES", the shading indicators should be:
- SHADE ABOVE → CALC: ▲
- SHADE BELOW → CALC: ▼
*(Note: The worksheet shows the opposite, which is likely an error.)*