Question

on #3 - 5, you must show your work to earn credit even though it is multiple - choice.

1. each dot in the scatterplot represents the height x, in feet, in the high jump and the distance y, in feet, in the long jump made by each student in a group of twenty students. the graph of which of the following equations is a line that most closely fits the data?

a. y = 0.82x + 3.30
b. y = 0.82x - 0.82
c. y = 3.30x + 0.82
d. y = 3.30x - 3.30

1. citrus production in china (2006 - 2014)

the scatterplot above shows the citrus production, in millions of metric tons, in china from 2006 through 2014. which of the following could be the slope of a line of best fit for the data?
a. 2.12
b. 5.25
c. 7.80
d. 10.29

1. the scatterplot below shows a company’s ice cream sales d, in dollars, and the high temperature t, in degrees celsius (°c), on 12 different days. a line of best fit for the data is also shown. which of the following could be an equation of the line of best fit?

a. d = 0.03t + 402
b. d = 10t + 402
c. d = 33t + 300
d. d = 33t + 84

Explanation:

Step1: Analyze problem 3

We need to find the line - of - best - fit equation for the high - jump and long - jump data. We can estimate the slope and y - intercept by looking at the general trend of the scatter - plot. The line should pass through the middle of the data points. A reasonable estimate of the slope is a non - large positive value.

Step2: Evaluate options for problem 3

For option A: $y = 0.82x+3.30$, the slope $m = 0.82$ and y - intercept $b = 3.30$. This seems reasonable as the data has a positive correlation and the y - intercept is positive. For option B: $y = 0.82x - 0.82$ has a negative y - intercept which doesn't seem to fit the data. For option C: $y = 3.30x+0.82$, the slope is too large. For option D: $y = 3.30x - 3.30$ has a large slope and a negative y - intercept which is not appropriate. So the answer for problem 3 is A.

Step3: Analyze problem 4

We need to estimate the slope of the line of best fit for the citrus production data. We can pick two points on the line of best fit (estimated visually). Let's assume the line passes through $(0, 20)$ and $(8, 35)$ (approximate points). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1 = 20,x_2 = 8,y_2 = 35$. Then $m=\frac{35 - 20}{8-0}=\frac{15}{8}=1.875$. The closest value to this among the options is A. 2.12.

Step4: Analyze problem 5

We need to find the equation of the line of best fit for the ice - cream sales data. We can estimate the slope and y - intercept by looking at two points on the line. Let's take $(12,500)$ and $(24,900)$. The slope $m=\frac{900 - 500}{24 - 12}=\frac{400}{12}\approx33$. When $t = 12$, if we substitute into $d=33t + 84$, we get $d=33\times12+84=396 + 84 = 480$ (close to the value on the graph). For $d = 0.03t+402$, the slope is too small. For $d = 10t+402$, the slope is too small. For $d = 33t+300$, when $t = 12$, $d=33\times12 + 300=396+300 = 696$ which is not as close as $d = 33t + 84$. So the answer for problem 5 is D.

Answer:

1. A. $y = 0.82x+3.30$
2. A. 2.12
3. D. $d = 33t + 84$