Question

the following is data for the first and second quiz scores for 8 students in a class.
first quiz\tsecond quiz
14\t11
15\t15
23\t17
26\t24
31\t28
37\t32
46\t42
47\t43
plot the points in the grid below, then sketch a line that best fits the data.
grid with y - axis 5 - 50, x - axis 0 - 50, and drawing tools
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Explanation:

Step1: Identify Coordinates

For each student, the first quiz score is the x - coordinate and the second quiz score is the y - coordinate. The points are: (14, 11), (15, 15), (23, 17), (26, 24), (31, 28), (37, 32), (46, 42), (47, 43).

Step2: Plot Points

On the given grid, find the x - value (first quiz score) on the horizontal axis and the y - value (second quiz score) on the vertical axis and mark each point. For example, for (14, 11), move 14 units along the x - axis (from 0) and 11 units along the y - axis and mark the point. Do this for all 8 points.

Step3: Sketch Best - Fit Line

A line of best fit should pass through the middle of the points, approximately balancing the number of points above and below the line. Looking at the trend, as the first quiz score (x) increases, the second quiz score (y) also increases. So we can draw a straight line that goes through or near the middle of the plotted points, such as a line with a positive slope that passes close to most of the points.

(Note: Since this is a plotting task, the final answer is the visual representation of the plotted points and the best - fit line. Here we describe the process. If we were to represent the line equation approximately, we can calculate the slope and intercept. Let's calculate the slope between two points, say (14, 11) and (47, 43). The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{43 - 11}{47 - 14}=\frac{32}{33}\approx0.97$. Using the point - slope form $y - y_1=m(x - x_1)$ with (14, 11), we get $y-11 = 0.97(x - 14)$, which simplifies to $y=0.97x-13.58 + 11=0.97x - 2.58$. But the main task is plotting.)

Answer:

1. Plot the points (14, 11), (15, 15), (23, 17), (26, 24), (31, 28), (37, 32), (46, 42), (47, 43) on the grid.
2. Sketch a straight line with a positive slope that passes through the middle of the plotted points (an approximate line of best fit).