Question

1. fast food and stress level

fast food should be a minimal part of any healthy diet. fast foods and junk foods are high in fat, sodium, and sugar, and the regular consumption of these can lead to a variety of health problems.
canadian researchers at the university of montreal found that mice which followed a high - fat diet felt more anxious after 6 weeks than rodents on a low - fat diet. the reason for this is that eating foods high in sugar and fat actually changes the chemical activity in your brain, causing signs of withdrawal and depression if you stop consuming them, according to the study. note, anxiety levels in mice were measured by how the mice reacted to being put in a new environment: did they explore the environment (low anxiety), or remain in a corner, frightened (high anxiety).
to further explore these results, a group of people were asked to state the number of times that she or he consumed fast food in the last month. each person was then given a questionnaire which measured the participants level of anxiety on a scale of 1 to 30 (where 1 represented the lowest level of anxiety and 30 represented the highest level of stress).
the results of this study are shown in the graph at right. (note, the relationship is accurate, but data is fictitious.)
refer to the scatter plot at right to answer the following questions.
(a) draw a line of best fit through the data points.
(b) is the correlation positive or negative?
(c) pick two points on the line and complete the table below.
(d) write an equation for the line of best fit. show all of your work, and simplify fractions completely.

Explanation:

Step1: Identify two points on the line

Let's take the points $(6,5)$ and $(16,10)$ from the line of best - fit.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $x_1 = 6,y_1 = 5,x_2=16,y_2 = 10$ gives $m=\frac{10 - 5}{16 - 6}=\frac{5}{10}=\frac{1}{2}$.

Step3: Use the point - slope form $y - y_1=m(x - x_1)$

Using the point $(6,5)$ and $m=\frac{1}{2}$, we have $y - 5=\frac{1}{2}(x - 6)$.

Step4: Convert to slope - intercept form $y=mx + b$

Expand the right - hand side: $y-5=\frac{1}{2}x-3$. Then add 5 to both sides to get $y=\frac{1}{2}x + 2$.

Answer:

(a) (This cannot be shown in text format, but the general idea is to draw a straight line that passes as close as possible to most of the data points on the scatter - plot.)
(b) Positive
(c) For example, the points $(6,5)$ and $(16,10)$
(d) $y=\frac{1}{2}x + 2$