Question

1. the scatter plot shows the size and annual rents of some office spaces in the downtown area of a city.

what would the line of best fit reveal about these data?
a. there is a strong negative relationship between the cost of rent and the size of the office space.
b. there is a weak positive relationship between the cost of rent and the size of the office space.
c. there is a strong positive relationship between the cost of rent and the size of the office space.
d. there is a weak negative relationship between the cost of rent and the size of the office space.

1. for which scatter plot would the line of best fit be represented by the equation $y = \frac{1}{2}x + 2$?

Explanation:

Question 43

To determine the relationship, we analyze the scatter plot. As office space size (x - axis) increases, annual rent (y - axis) also increases. The points seem to cluster closely around a line with a positive slope, indicating a strong positive relationship. Option a and d are negative, so incorrect. Option b says weak, but the clustering suggests strong. So option c is correct.

The equation is \(y=\frac{1}{2}x + 2\). The slope is positive (\(\frac{1}{2}\)) and y - intercept is 2. We check the scatter plots:

• For a positive slope, as x increases, y increases.
• The y - intercept is 2, so when \(x = 0\), \(y=2\). Also, the slope means for every increase of 2 in x, y increases by 1.

Looking at the plots, the first plot (let's assume it's option a) should have points that follow this trend: starting around y = 2 when x = 0 and increasing with a slope of 1/2. The other plots either have negative trends or don't match the intercept/slope. So the scatter plot with points showing a positive trend, starting near y = 2 and increasing with slope 1/2 is the one. (Assuming the first plot (a) matches this, as the other plots have negative or different slopes/intercepts)

Answer:

c. There is a strong positive relationship between the cost of rent and the size of the office space.

Question 44