Question

1. which situation does not describe a causal relationship?

(1) the higher the volume on a radio, the louder the sound will be.
(2) the faster a student types a research paper, the more pages the paper will have.
(3) the shorter the distance driven, the less gasoline that will be used.
(4) the slower the pace of a runner, the longer it will take the runner to finish the race.

1. the table below shows the number of grams of carbohydrates, x, and the number of calories, y, of six different foods.

which equation best represents the line of best fit for this set of data?
(1) y = 15x
(2) y = 0.07x
(3) y = 0.1x - 0.4
(4) y = 14.1x + 5.8

Explanation:

Step1: Calculate the ratio of \(y\) to \(x\) for each data point

For \((x = 8,y = 120)\), \(\frac{y}{x}=\frac{120}{8}=15\)
For \((x = 9.5,y = 138)\), \(\frac{y}{x}=\frac{138}{9.5}\approx14.53\)
For \((x = 10,y = 147)\), \(\frac{y}{x}=\frac{147}{10}=14.7\)
For \((x = 6,y = 88)\), \(\frac{y}{x}=\frac{88}{6}\approx14.67\)
For \((x = 7,y = 108)\), \(\frac{y}{x}=\frac{108}{7}\approx15.43\)
For \((x = 4,y = 62)\), \(\frac{y}{x}=\frac{62}{4}=15.5\)

Step2: Analyze each option

• Option (1): \(y = 15x\). When \(x = 8\), \(y=15\times8 = 120\); when \(x = 10\), \(y = 15\times10=150\) (close to \(147\)). But for \(x = 4\), \(y=15\times4 = 60\) (close to \(62\)).
• Option (2): \(y=0.07x\). When \(x = 8\), \(y=0.07\times8=0.56

eq120\).

• Option (3): \(y = 0.1x-0.4\). When \(x = 8\), \(y=0.1\times8 - 0.4=0.4

eq120\).

• Option (4): \(y=14.1x + 5.8\). When \(x = 8\), \(y=14.1\times8+5.8=112.8 + 5.8=118.6

eq120\); when \(x = 10\), \(y=14.1\times10+5.8=141+5.8 = 146.8\approx147\); when \(x = 4\), \(y=14.1\times4+5.8=56.4+5.8=62.2\approx62\)

Answer:

(1) \(y = 15x\)