Question 4·SAT Desmos Regression Practice·Problem Solving and Data Analysis

The dots run roughly straight downward from left to right. A negative slope means $y$ decreases as $x$ increases, so the model needs a negative number multiplying $x$.

Read each dot as $(x,y)$: the horizontal coordinate is $x$, and the vertical coordinate is $y$. Enter $(1,10)$, $(3,8)$, $(5,6)$, $(7,5)$, and $(9,2)$ in a Desmos table. Keep each dot’s coordinates in the same row so Desmos fits the plotted data.

Type $y_1\sim mx_1+b$. The symbol $\sim$ tells Desmos to run a regression, finding the line that best fits the table. Under PARAMETERS, it shows $m=-0.95$ and $b=10.95$. The dots don’t all lie on one line, so the model follows the overall trend, not every dot.

The fitted slope $-0.95$ is closer to $-0.9$ than to $-1.1$. The fitted intercept $10.95$ is positive and close to $10.5$. So the most appropriate linear model for the scatterplot is $y=-0.9x+10.5$. Choice A.

The dots fall as $x$ increases, so the slope must be negative. A $y$-intercept is the line’s predicted height at $x=0$. Since the dot at $(1,10)$ is already near $10$, extending the falling trend one unit left puts that intercept above $10$. That leaves the two equations with a negative slope and $+10.5$.

Use the dot $(9,2)$ because a larger $x$ makes the difference between the two slopes easier to see. Type $-0.9(9)+10.5$ and $-1.1(9)+10.5$ in Desmos. It shows $2.4$ and $0.6$, respectively. $2.4$ is closer to the plotted $y$-value $2$, so $y=-0.9x+10.5$ better follows the points. Choice A.