Question

The average score on a national assessment test for a subject was 194 points for​ fourth-graders who studied the subject about 45 minutes per week. The average score was 211 points for​ fourth-graders who studied the subject about 150 minutes per week. There is an approximate linear relationship between the number of hours​ fourth-graders study the subject per week and the average score on the test. Estimate the average score for​ fourth-graders who study the subject about 235 minutes per week.

Answer 1

The average score for​ fourth-graders who study the subject about 235 minutes per week is 224.76.

Explanation:

Let x be the number of hours​ fourth-graders study the subject per week and y be the average score on the test. It is given that there is an approximate linear relationship between x and y.

It is given that the average score on a national assessment test for a subject was 194 points for​ fourth-graders who studied the subject about 45 minutes per week. It means the line passes through (45, 194).

The average score was 211 points for​ fourth-graders who studied the subject about 150 minutes per week. It means the line passes through (150, 211).

If a line passes through two points then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The equation of required line is

`y-194=(211-194)/(150-45)(x-45)`

`y-194=(17)/(105)(x-45)`

Using distributive property,

`y-194=(17)/(105)(x)-(17)/(105)(45)`

`y-194=(17)/(105)(x)-(51)/(7)`

Add 194 on both sides.

`y=(17)/(105)(x)-(51)/(7)+194`

`y=(17)/(105)(x)+(1307)/(7)`

Substitute x=235 in the above equation.

`y=(17)/(105)(235)+(1307)/(7)`

`y=(799)/(21)+(1307)/(7)`

`y=(4720)/(21)`

`y=224.7619`

`y\approx 224.76`

Therefore the average score for​ fourth-graders who study the subject about 235 minutes per week is 224.76.