Question

The table shows the average daily high temperature in a city each each week for eight weeks after the first day of spring. Which of the following is an appropriate line of fit for the data? Use the line of fit to find the approximate temperature on the first day of spring and the average rate of change in temperature. Week, 2 1 2 3 4 5 6 7 8 Average Daily High Temperature, y (°F) 56 57 59 61 62 64 66 68 Oy= 22 + 56 Oy= -1.72 +54 Oy= 2.62 +56 Oy= 1.7x + 54 The temperature on the first day of spring was about E. The average rate of change in temperature is about °F per week.

Answer 1

Let's begin by listing out the information given to us:

Temperature is a function of the week number; the week is the independent variable while the temperature is the dependent variable

$(x,y)=(1,56),(2,57),(3,59),(4,61),(5,62),(6,64),(7,66),(8,68)$

We will proceed to plot the graph & identify the line of fit:

The approximate temperature on the first day of spring is 55.5 degrees Fahrenheit

The average rate of change in temperature is given by:

$\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{66-59}{7-3}=\frac{7}{4}=1.75 \\ m=1.75^{\circ}F\text{/we}ek \end{gathered}$