Question

est: function concepts
7
select the correct answer.
the graph shows a relationship between the size of 18 households and the average amount of time, in hours, each member of the household spends on chores per week.
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 graph shows a negative correlation (as x increases, y decreases), so the slope should be negative. Eliminate options B and D (their slopes are positive: 0.34).

Step2: Analyze the y-intercept

When x = 0, the y - intercept should be positive (the line crosses the y - axis above 0). Option A has a y - intercept of - 5.19 (negative), option C has a y - intercept of 5.19 (positive). Also, the slope of - 0.34 in option C makes sense for the negative trend.

Answer:

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