SAT Question 2e8027b0: Two-variable Data Models And Scatterplots answer and explanation with Desmos solution

Choice A is correct. An equation of a line of best fit for data set F can be written in the form $y=a+bx$, where $a$ is the y-coordinate of the y-intercept of the line of best fit and $b$ is the slope. The line of best fit shown for data set E has a y-intercept at approximately $\left(0,12\right)$. It's given that data set F is created by multiplying the y-coordinate of each data point from data set E by $3.9$. It follows that a line of best fit for data set F has a y-intercept at approximately $\left(0,12\left(3.9\right)\right)$, or $\left(0,46.8\right)$. Therefore, the value of $a$ is approximately $46.8$. The slope of a line that passes through points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ can be calculated as $\frac{y_2-y_1}{x_2-x_1}$. Since the line of best fit shown for data set E passes approximately through the point $\left(12,30\right)$, it follows that a line of best fit for data set F passes approximately through the point $\left(12,30\left(3.9\right)\right)$, or $\left(12,117\right)$. Substituting $\left(0,46.8\right)$ and $\left(12,117\right)$ for $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$, respectively, in $\frac{y_2-y_1}{x_2-x_1}$ yields $\frac{117-46.8}{12-0}$, which is equivalent to $\frac{70.2}{12}$, or $5.85$. Therefore, the value of $b$ is approximately $5.85$, or approximately $5.9$. Thus, $y=46.8+5.9x$ could be an equation of a line of best fit for data set F.