Question

A teacher observed that the average test scores for her class increased during the course of the year. The average score for each of the six tests she gave throughout the year are shown in the table. The table is titled average test scores. The table has two columns and six rows. The first column is labeled test number and the second column is labeled average score. Test one, seventy-six and five tenths. Test two, seventy-nine and zero tenths. Test three, eighty-one and five tenths. Test four, eighty-four and zero tenths. Test five, eighty-six and five tenths. Test six, eighty-nine and zero tenths. If y represents the average test score and x represents the test number, which linear function BEST fits the data in the table? Responses

Answer 1

The best linear function to fit the given data of average test scores versus test number is y = 2.5x + 74, where x represents the test number and y represents the average test score.

Step-by-step explanation:

To find the linear function that best fits the given data for a class's average test scores, we will use the data points provided in the table. The test scores represent the dependent variable y, and the test numbers represent the independent variable x.

To establish the linear relationship, we note that as x increases by 1 (moving from one test to the next), the average score y consistently increases by 2.5 points.

A linear function is typically in the form y = mx + b, where m is the slope and b is the y-intercept. By analyzing the provided scores, we can observe that the initial score (for Test 1, when x = 1) was 76.5. This value will act as our starting point for calculating b, the y-intercept, since this is the score when we would theoretically start at Test number 0.

Our slope (m) is the consistent score increase, which as noted is 2.5 points per test. Therefore, the equation of the line of best fit, given this slope and starting value, is y = 2.5x + 74. This equation assumes that the pattern of increase will continue in a linear fashion.