The function \( h(t) = \frac{t}{3} \) describes a linear relationship between the input variable \( t \) and the output \( h(t) \). The graph of this function will be a straight line with a slope of \( \frac{1}{3} \), meaning that for every unit increase in \( t \), \( h(t) \) increases by \( \frac{1}{3} \).

### Key Characteristics:
1. **Slope (m)**: The slope of the line is \( \frac{1}{3} \), indicating the rate of change of \( h(t) \) with respect to \( t \).
2. **Y-intercept (b)**: Since there is no constant term added to \( \frac{t}{3} \), the y-intercept is \( 0 \). This means the line passes through the origin (0,0).
3. **Domain and Range**: The domain (set of possible input values for \( t \)) is all real numbers, \( (-\infty, \infty) \). Similarly, the range (set of possible output values for \( h(t) \)) is also all real numbers, \( (-\infty, \infty) \).

### Graph Interpretation:
- The graph will be a straight line starting at the origin and rising with a gentle slope of \( \frac{1}{3} \).
- As \( t \) increases, \( h(t) \) increases at a rate of one-third of the change in \( t \).

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### Relative Questions:
1. What is the slope of a line, and how does it affect the graph?
2. How do you determine the y-intercept of a linear function?
3. What happens to the graph of \( h(t) \) if the slope changes?
4. How would you graph the function \( h(t) = \frac{t}{3} + 2 \)?
5. How does the function \( h(t) = \frac{t}{3} \) compare to \( h(t) = 3t \)?

### Tip:
For linear functions, the slope indicates the steepness of the line, and the y-intercept shows where the line crosses the y-axis.

Explore the linear function h(t) = t/3, which describes a straight line with a slope of 1/3 and a y-intercept of 0. Learn how to graph the function and understand key characteristics such as slope, y-intercept, domain, and range. Suitable for students in Grades 8-10.

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