Once you have the slope $b$, you can avoid solving for the y-intercept directly by using the formula $\hat y = \bar y + b(x - \bar x)$. What are $\bar x$ and $\bar y$ from the table?

After you set up $\hat y = \bar y + b(x - \bar x)$, plug in $x = 8$ along with the values for $\bar x$, $\bar y$, and $b$, then simplify.

When you compute the predicted $\hat y$, you will get a decimal value. Make sure to round that value to the nearest whole number before matching it to the answer choices.

In a new expression line, type b = 0.76*(9/1.2) and press Enter. Desmos will display the numerical value of b, which is the slope of the regression line.

In the next line, type yhat(x) = 48 + b*(x - 5.5). This defines the predicted weekly energy consumption $\hat y$ as a function of the average daily active hours $x$.

In a new line, type yhat(8) and press Enter. The value that appears to the right is the predicted weekly energy consumption for a sensor active 8 hours per day; round this value to the nearest whole number and match it to the closest answer choice.

For the least-squares regression line predicting $y$ from $x$:

• The slope is $b = r\dfrac{s_y}{s_x}$.
• A convenient form of the line is

where $\bar x$ and $\bar y$ are the means of $x$ and $y$.

Use $r = 0.76$, $s_y = 9$, and $s_x = 1.2$:

Compute the fraction first:

Then multiply:

So the slope of the regression line is $5.7$.

We know $\bar x = 5.5$, $\bar y = 48$, and $b = 5.7$. Plug these into

to get

The question asks for the predicted weekly energy consumption when the sensor is active an average of 8 hours per day, so substitute $x = 8$ into the regression equation:

Simplify the parentheses:

so

Now multiply and add:

so

Rounding $62.25$ to the nearest watt-hour gives $62$.

Therefore, the predicted weekly energy consumption is $62$ watt-hours, which corresponds to choice B.