Question

Which of these linear equations best describes the given model? Choose 1 answer: Choose 1 answer: (Choice A) A \hat y=10x+20 y ^ ​ =10x+20y, with, hat, on top, equals, 10, x, plus, 20 (Choice B, Checked) B \hat y=20x+20 y ^ ​ =20x+20y, with, hat, on top, equals, 20, x, plus, 20 (Choice C) C \hat y=-20x+20 y ^ ​ =−20x+20y, with, hat, on top, equals, minus, 20, x, plus, 20 Based on this equation, estimate the score for a student that spent 3.83.83, point, 8 hours studying.

Answer 1

Question:

Which of these linear equations best describes the given model? Choose 1 answer:

Choose 1 answer:

A $\hat y=10x+20$

B $\hat y=20x+20$

C $\hat y=-20x+20$

Based on this equation, estimate the score for a student that spent 3.8 hours studying.

Answer:

$\hat y = 20x +20$

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:

$(x_1,y_1) = (0,20)$

$(x_2,y_2) = (2,60)$

The slope (m) is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{60 - 20}{2 - 0}$

$m = \frac{40}{2}$

$m = 20$

The equation is calculated using:

$\hat y = m(x - x_1) + y_1$

This gives:

$\hat y = 20(x - 0) +20$

$\hat y = 20(x ) +20$

$\hat y = 20x +20$

Solving (b): When study hours is 3.8

This means that $x= 3.8$

So:

$\hat y = 20x +20$

$\hat y = 20 * 3.8 + 20$

$\hat y = 96$