Question

the scatterplot shows the relationship between two variables, x and y.
which of the following equations is the most appropriate linear model for the data shown?
a) $y = 0.9 + 9.4x$
b) $y = 0.9 - 9.4x$
c) $y = 9.4 + 0.9x$
d) $y = 9.4 - 0.9x$

Explanation:

Step1: Identify slope direction

As $x$ increases, $y$ decreases, so slope is negative. Eliminate options A and C (positive slopes).

Step2: Find y-intercept estimate

When $x=0$, $y=10$. The y-intercept in the equation is the constant term. Option B has intercept 0.9 (too low), Option D has intercept 9.4 (close to 10).

Step3: Verify slope magnitude

The slope of -0.9 matches the gradual downward trend (y decreases ~0.9 per 1-unit x increase).

Answer:

D) $y = 9.4 - 0.9x$