Question

which of the following equations is the most appropriate linear model for the data shown in the scatterplot? a) $y = -1.9x - 10.1$ b) $y = -1.9x + 10.1$ c) $y = 1.9x - 10.1$ d) $y = 1.9x + 10.1$

Explanation:

Step1: Identify slope direction

The scatterplot shows y decreasing as x increases, so the slope is negative. This eliminates options C and D, which have positive slopes ($1.9$).

Step2: Analyze y-intercept

The line should cross the y-axis (when $x=0$) at a positive value, since when $x=0$, the corresponding y-value is ~9.5. For option A, $y=-1.9(0)-10.1=-10.1$ (negative y-intercept, does not match). For option B, $y=-1.9(0)+10.1=10.1$ (positive y-intercept, matches the data's trend).

Answer:

B) $y = -1.9x + 10.1$