Find the line of best fit for the following data using a graphing calculator. Use the indicated variables and proper function notation in your answer. Round to 3 decimal places as... Find the line of best fit for the following data using a graphing calculator. Use the indicated variables and proper function notation in your answer. Round to 3 decimal places as needed. t 1 2 3 4 5 6 h(t) 800 761 825 841 825 825 Read more

Steps to Solve

1. Input the data into the graphing calculator

Enter the values of $t$ into list L1 and the values of $h(t)$ into list L2 in your graphing calculator. To do this, press STAT, then select 1:Edit.

2. Calculate the linear regression equation

Press STAT, then move to CALC and select 4:LinReg(ax+b). Specify L1 as the Xlist and L2 as the Ylist. Calculate to obtain the values for $a$ (slope) and $b$ (y-intercept).

3. Write the equation in slope-intercept form

The graphing calculator will output the values of $a$ and $b$ for the linear regression equation $y = ax + b$. In this case, we are using the variables $t$ and $h(t)$, so we can write the equation as $h(t) = at + b$.

4. Substitute the calculated values and round

Substitute the values of $a$ and $b$ obtained from the calculator into the equation $h(t) = at + b$. Round the values of $a$ and $b$ to three decimal places as specified in the question.

Using a TI-84 calculator, I get the values $a = 9.714$ and $b = 781.571$.

Therefore, the equation is $h(t) = 9.714t + 781.571$.