SAT Question 9b9da812: Two-variable Data Models And Scatterplots answer and explanation with Desmos solution

Choice C is correct. A linear model can be written in the form $y=mx+b$, where $m$ is the slope of the graph of the model in the xy-plane and $(0,b)$ is the y-intercept. The graph of an appropriate linear model for the data shown in the scatterplot passes near the points $(0,0)$ and $(4,2.4)$ in the xy-plane. Two points on a line, $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$, can be used to find the slope of the line using the slope formula, $m=\frac{y_2-y_1}{x_2-x_1}$. Substituting the points $(0,0)$ and $(4,2.4)$ for $\left(x_{1,}{y}_1\right)$ and $\left(x_2,y_2\right)$, respectively, in the slope formula yields $m=\frac{2.4-0}{4-0}$, or $m=0.60$. Therefore, the value of $m$ for an appropriate linear model is approximately $0.60$. Substituting $0.60$ for $m$ in $y=mx+b$ yields $y=0.60x+b$. Since an appropriate linear model passes near the point $(0,0)$, it follows that $b$ is approximately $0$ and an appropriate linear model for the data is $y=0.60x+0$. Thus, of the given choices, $y=0.606x$ is the most appropriate linear model for these data.

Alternate approach: A linear model can be written in the form $y=mx+b$, where $m$ is the slope of the graph of the model in the xy-plane and $(0,b)$ is the y-intercept. The scatterplot shows that as the x-values of the data points increase, the y-values of the data points increase, which means the graph of an appropriate linear model has a positive slope. The scatterplot also shows that an appropriate linear model would pass close to the point $(0,0)$. Of the given choices, $y=0.606x$ is the only linear model whose graph has a positive slope and a y-intercept of $(0,0)$.