Question

time spent on chores (hours)
household members
which equation best models this data set?
a. $y = 0.34x + 5.19$
b. $y = -0.34x - 5.19$
c. $y = -0.34x + 5.19$
d. $y = 0.34x - 5.19$

Explanation:

Step1: Analyze the slope

The line in the scatter plot is decreasing, so the slope (m) should be negative. Let's check the options:

• Option A: Slope is 0.34 (positive) → Eliminate.
• Option D: Slope is 0.34 (positive) → Eliminate.

Step2: Analyze the y - intercept

When x = 0, the y - intercept (b) should be positive (since at x = 0, y is around 5).

• Option B: y - intercept is - 5.19 (negative) → Eliminate.
• Option C: Slope is - 0.34 (negative, matches the decreasing line) and y - intercept is 5.19 (positive, matches the graph when x = 0).

Answer:

C. \( y = -0.34x + 5.19 \)