Question

part 2 of 4
(b) use the equation to approximate the average amount spent per person in year 1 and compare it with the actual amount spent of $48.13. the average amount spent per person in year 1 was approximately $45. the approximate value differs from the actual value by $3.13.
part 3 of 4
(c) what is the slope of the line and what does it mean in the context of this problem? the slope is 9.4. the amount spent per person on video games increased by an average rate of $9.4 per year.
part: 3 / 4
part 4 of 4
(d) what is the y - intercept and what does it mean in the context of this problem? write the intercept as an ordered pair. the y - intercept is. the y - intercept means that the average amount spent on video games per person was $ at the start of the study (year )

Explanation:

Step1: Recall the form of a linear - equation

The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. In the context of the problem, $y$ represents the average amount spent per person on video - games and $x$ represents the year.

Step2: Use the information from part (b)

In part (b), when $x = 1$, $y\approx45$. In part (c), $m = 9.4$. Substitute $x = 1$, $y\approx45$ and $m = 9.4$ into $y=mx + b$. So, $45=9.4\times1 + b$.

Step3: Solve for $b$

Rearrange the equation $45 = 9.4\times1 + b$ to solve for $b$. We get $b=45 - 9.4=35.6$.

Answer:

The $y$-intercept is $(0,35.6)$. The $y$-intercept means that the average amount spent on video games per person was $\$35.6$ at the start of the study (year $0$).