Use the formula $b = \dfrac{n\Sigma xy - (\Sigma x)(\Sigma y)}{n\Sigma x^2 - (\Sigma x)^2}$. Write expressions for the numerator and denominator using the given numbers, but do not simplify yet.

Now compute the products in the numerator and denominator, subtract to get each, then form the fraction for the slope and convert your final answer to a decimal.

In Desmos, type the expression (6*1380 - 30*228) / (6*200 - 30^2) exactly, using the given summary statistics in place of $n$, $\Sigma x$, $\Sigma y$, $\Sigma x^2$, and $\Sigma xy$.

Look at the numeric value Desmos displays for this expression; that value is the slope of the least-squares regression line. Match this value to the closest choice in the answer options.

For a least-squares regression line predicting $y$ from $x$, and given summary statistics $n$, $\Sigma x$, $\Sigma y$, $\Sigma x^2$, and $\Sigma xy$, the slope $b$ is

Here, $x$ is age (weeks) and $y$ is height (centimeters). We will plug in the given numbers to this formula.

We are given:

• $n = 6$
• $\Sigma x = 30$
• $\Sigma y = 228$
• $\Sigma x^2 = 200$
• $\Sigma xy = 1{,}380$

Substitute into the formula.

First, the numerator:

Compute each product:

• $6 \cdot 1{,}380 = 8{,}280$
• $30 \cdot 228 = 6{,}840$

So the numerator is:

Now the denominator:

Compute each part:

• $6 \cdot 200 = 1{,}200$
• $(30)^2 = 900$

So the denominator is:

Now plug the numerator and denominator into the slope formula:

Simplify this fraction:

• Divide numerator and denominator by 10: $\frac{1{,}440}{300} = \frac{144}{30}$
• Divide both by 6: $\frac{144}{30} = \frac{24}{5}$

Now write $\frac{24}{5}$ as a decimal:

So, the slope of the least-squares regression line that predicts height from age is 4.8, which corresponds to choice B.