shiras math test included a survey question asking how many hours students spent studying for the test. the…

shiras math test included a survey question asking how many hours students spent studying for the test. the scatter plot below shows the relationship between how many hours students spent studying and their score on the test. a line was fit to the data to model the relationship. which of these linear equations best describes the given model? choose 1 answer: \na $hat{y}=x + 45$\nb $hat{y}=10x + 45$\nc $hat{y}=-10x + 45$

shiras math test included a survey question asking how many hours students spent studying for the test. the scatter plot below shows the relationship between how many hours students spent studying and their score on the test. a line was fit to the data to model the relationship. which of these linear equations best describes the given model? choose 1 answer: \na $hat{y}=x + 45$\nb $hat{y}=10x + 45$\nc $hat{y}=-10x + 45$

Answer

Explanation:

Step1: Find the y - intercept

The line intersects the y - axis around $y = 45$. So the y - intercept $b$ of the line of best - fit is approximately 45.

Step2: Estimate the slope

Pick two points on the line. Let's take $(0,45)$ and $(4,85)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{85 - 45}{4-0}=\frac{40}{4}=10$.

Step3: Write the equation

The equation of a line in slope - intercept form is $\hat{y}=mx + b$. Substituting $m = 10$ and $b = 45$, we get $\hat{y}=10x + 45$.

Answer:

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