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The problem provided in the image asks to determine the unknown values in the table using the equation:

\[
h = -2.3t + 18.9
\]

where \( h \) and \( t \) are related.

The table shows some values of \( t \) and \( h \) as:

| \( t \)  | \( h \)  |
|---------|---------|
| -2      | ?       |
| ?       | 21.2    |
| 1.6     | ?       |
| ?       | 12      |

Let's solve for the unknown values:

### 1. When \( t = -2 \), find \( h \):
\[
h = -2.3(-2) + 18.9 = 4.6 + 18.9 = 23.5
\]
So, \( h = 23.5 \).

### 2. When \( h = 21.2 \), find \( t \):
Using the equation \( h = -2.3t + 18.9 \), solve for \( t \):
\[
21.2 = -2.3t + 18.9
\]
Subtract 18.9 from both sides:
\[
21.2 - 18.9 = -2.3t \implies 2.3 = -2.3t
\]
Divide both sides by -2.3:
\[
t = \frac{2.3}{-2.3} = -1
\]
So, \( t = -1 \).

### 3. When \( t = 1.6 \), find \( h \):
\[
h = -2.3(1.6) + 18.9 = -3.68 + 18.9 = 15.22
\]
So, \( h = 15.22 \).

### 4. When \( h = 12 \), find \( t \):
\[
12 = -2.3t + 18.9
\]
Subtract 18.9 from both sides:
\[
12 - 18.9 = -2.3t \implies -6.9 = -2.3t
\]
Divide both sides by -2.3:
\[
t = \frac{-6.9}{-2.3} = 3
\]
So, \( t = 3 \).

### Final Table:

| \( t \)  | \( h \)  |
|---------|---------|
| -2      | 23.5    |
| -1      | 21.2    |
| 1.6     | 15.22   |
| 3       | 12      |

---

Would you like further details on any of these steps?

### Follow-up Questions:
1. Can you solve a similar equation for different values of \( t \) and \( h \)?
2. How would the slope (-2.3) affect the values of \( h \) for large values of \( t \)?
3. Can you graph the equation \( h = -2.3t + 18.9 \) and interpret its slope and intercept?
4. What is the significance of the intercept 18.9 in this equation?
5. How can you verify the solution using a calculator or a graphing tool like Desmos?

**Tip:** When solving linear equations like this, isolating the variable of interest helps simplify the steps.

The equation h = -2.3t + 18.9 relates h and t. Use the equation to determine the unknown values in the table. Show all work.

Solve for unknown values in the equation h = -2.3t + 18.9 with a step-by-step solution. This problem covers solving linear equations and filling in a table for missing values. Suitable for students in Grades 9-11.

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