Respuesta :
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
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The equation of required line is
[tex]y-194=\frac{211-194}{150-45}(x-45)[/tex]
[tex]y-194=\frac{17}{105}(x-45)[/tex]
Using distributive property,
[tex]y-194=\frac{17}{105}(x)-\frac{17}{105}(45)[/tex]
[tex]y-194=\frac{17}{105}(x)-\frac{51}{7}[/tex]
Add 194 on both sides.
[tex]y=\frac{17}{105}(x)-\frac{51}{7}+194[/tex]
[tex]y=\frac{17}{105}(x)+\frac{1307}{7}[/tex]
Substitute x=235 in the above equation.
[tex]y=\frac{17}{105}(235)+\frac{1307}{7}[/tex]
[tex]y=\frac{799}{21}+\frac{1307}{7}[/tex]
[tex]y=\frac{4720}{21}[/tex]
[tex]y=224.7619[/tex]
[tex]y\approx 224.76[/tex]
Therefore the average score for fourth-graders who study the subject about 235 minutes per week is 224.76.
