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The image asks to "Write the slope-intercept form equation for the situation":

The temperature was 65°F 5 hours ago. If the temperature was 0°F, `t` represents the change in temperature, and `x` represents the change in hours since then.

Let's break down the problem step-by-step:

1. **Identify the variables:**
   - \( x \): the number of hours since 5 hours ago.
   - \( t \): the temperature change.

2. **Find the initial temperature:**
   - The initial temperature \( t \) was 65°F, and 5 hours ago means \( x = 0 \) when the temperature was 65°F.
   - The temperature then changed to 0°F. This implies a decrease of 65°F over a span of 5 hours.

3. **Calculate the slope:**
   - The slope represents the rate of change of temperature over time.
   - Slope \( m = \frac{\text{change in temperature}}{\text{change in time}} = \frac{0 - 65}{5 - 0} = -13 \).

4. **Write the slope-intercept form equation:**
   - The slope-intercept form is \( y = mx + b \).
   - Here, \( t = -13x + 65 \) (where \( m = -13 \) and \( b = 65 \)).

### Final Equation:
\[ t = -13x + 65 \]

Would you like more details or have any questions?

### 5 Questions to Expand:
1. How do you interpret the slope in the context of temperature change?
2. What would happen to the equation if the temperature were different initially?
3. Can you convert the equation into another form, such as point-slope form?
4. How would you find the x-intercept of this equation, and what does it represent?
5. How does this equation change if the rate of temperature change were constant but at a different value?

**Tip:** In any word problem involving linear relationships, always identify the initial value and rate of change to form the equation correctly.

Write the slope-intercept form equation for the situation: The temperature was 65°F 5 hours ago. If the temperature was 0°F, t represents the change in temperature, and x represents the change in hours since then.

Learn how to write the slope-intercept form equation for a situation involving temperature change over time. This problem explores the key concepts of linear equations, including slope and intercept. Suitable for students in Grades 8-10.

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