Question

For the given linear function, make a table of h(t)=(1)/(2)-(6)/(7)t

Answer 1

To create a table for the linear function h(t), select values for t and calculate the corresponding h(t). Repeat for additional values and use the table to find the slope of the function.

Step-by-step explanation:

To create a table for the linear function h(t) = \( \frac{1}{2} - \frac{6}{7}t \), select values for t and calculate the corresponding h(t) values:

• Let t = 0: h(0) = \( \frac{1}{2} - \frac{6}{7}(0) = \frac{1}{2} \)
• Let t = 1: h(1) = \( \frac{1}{2} - \frac{6}{7}(1) = \frac{1}{2} - \frac{6}{7} = \frac{-1}{14} \)
• Let t = 2: h(2) = \( \frac{1}{2} - \frac{6}{7}(2) = \frac{1}{2} - \frac{12}{7} = \frac{-17}{14} \)

Repeat this process for additional values of t to fill in the table. To find the slope of the linear function, you can use two points from the table. For example, using t = 0 and t = 1, the slope can be calculated as the change in h(t) divided by the change in t, which is -\(\frac{6}{7}\).