Question

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: Identify slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Determine the sign of the slope

The line in the graph is decreasing, so the slope $m$ is negative. Options A and B have positive slopes, so they can be eliminated.

Step3: Estimate the y - intercept

The line intersects the y - axis above the origin. For option C, $y=- 0.34x - 5.19$ has a negative y - intercept ($b=-5.19$). For option D, $y=-0.34x + 5.19$ has a positive y - intercept ($b = 5.19$).

Answer:

D. $y=-0.34x + 5.19$