Question:
Which of these linear equations best describes the given model? Choose 1 answer:
Choose 1 answer:
A [tex]\hat y=10x+20[/tex]
B [tex]\hat y=20x+20[/tex]
C [tex]\hat y=-20x+20[/tex]
Based on this equation, estimate the score for a student that spent 3.8 hours studying.
Answer:
[tex]\hat y = 20x +20[/tex]
Score of 96 for studying 3.8 hours
Step-by-step explanation:
Given
See attachment for graph
From the straight line of trend, we have:
[tex](x_1,y_1) = (0,20)[/tex]
[tex](x_2,y_2) = (2,60)[/tex]
The slope (m) is:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{60 - 20}{2 - 0}[/tex]
[tex]m = \frac{40}{2}[/tex]
[tex]m = 20[/tex]
The equation is calculated using:
[tex]\hat y = m(x - x_1) + y_1[/tex]
This gives:
[tex]\hat y = 20(x - 0) +20[/tex]
[tex]\hat y = 20(x ) +20[/tex]
[tex]\hat y = 20x +20[/tex]
Solving (b): When study hours is 3.8
This means that [tex]x= 3.8[/tex]
So:
[tex]\hat y = 20x +20[/tex]
[tex]\hat y = 20 * 3.8 + 20[/tex]
[tex]\hat y = 96[/tex]
