Answer: B. y = 20x +20
The score for a student that spent 3.8 hours studying is expected to be 96.
Step by step solution:
The point-slope form of a linear equation is y = mx + b, where m is the slope and b the intercept with the y-axis.
To find the line that fits the data and model the relationship, we need to find the slope. Let
y = Test score
x = Study time (hours)
[tex]\begin{gathered} m=\frac{y_1-y_2}{x_1-x_2} \\ (x_1,y_1_{})\text{ and }(x_2,y_2)\text{ Point in the line} \end{gathered}[/tex]
Two pair of coordinates from the line are (2, 60) and (3, 80):
[tex]m=\frac{60-80}{2-3}=\frac{-20}{-1}=20[/tex]
We have m = 20, and b = 20 (intercept with the y-axis)
The equation that model the relationship is:
[tex]y=20x+20[/tex]
Second Part. Basing ourselves on the above equation, estimate the score for a student that spent 3.8 hours studying x = 3.8.
[tex]\begin{gathered} y=(20\cdot3.8)+20 \\ y=76+20 \\ y=96 \end{gathered}[/tex]
The score for a student that spent 3.8 hours studying is expected to be 96.
