Question

which of these linear equations best describes the given model? choose 1 answer: a $hat{y}=x + 45$ b $hat{y}=10x + 45$ c $hat{y}=-10x + 45$ based on this equation, estimate the score for a student that spent 5 hours studying.

Explanation:

Step1: Identify slope - intercept form

The general form of a linear equation is $\hat{y}=mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Determine y - intercept

The line intersects the y - axis (when $x = 0$) around $y=45$, so $b = 45$.

Step3: Estimate slope

As $x$ (study time) increases by 1 unit, $y$ (score) increases by approximately 10 units. So the slope $m = 10$. The equation is $\hat{y}=10x + 45$.

Step4: Estimate score for 5 hours

Substitute $x = 5$ into $\hat{y}=10x + 45$. Then $\hat{y}=10\times5+45=50 + 45=95$.

Answer:

1. B. $\hat{y}=10x + 45$
2. 95