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 $t$.

Would you like to go into more detail about any aspect of this function?

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.