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

Answer:

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

Step-by-step 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

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of required line is

$y-194=\frac{211-194}{150-45}(x-45)$

$y-194=\frac{17}{105}(x-45)$

Using distributive property,

$y-194=\frac{17}{105}(x)-\frac{17}{105}(45)$

$y-194=\frac{17}{105}(x)-\frac{51}{7}$

Add 194 on both sides.

$y=\frac{17}{105}(x)-\frac{51}{7}+194$

$y=\frac{17}{105}(x)+\frac{1307}{7}$

Substitute x=235 in the above equation.

$y=\frac{17}{105}(235)+\frac{1307}{7}$

$y=\frac{799}{21}+\frac{1307}{7}$

$y=\frac{4720}{21}$

$y=224.7619$

$y\approx 224.76$

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