Question

sec 2.4 applications of linear equations and modeling question 5 of 11 (1 point) 1 question attempt 1 of 3 part 1 of 4 (a) use the equation to approximate the average amount spent per person in year 2. the average amount spent per person in year 2 was approximately $54.4. 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. the amount spent per person on video games select by an average rate of $ per year.

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope. In the context of a linear model for spending over years, the slope represents the rate of change of the amount spent per person per year. Since we are not given the equation in the problem statement, assume we have two points $(x_1,y_1)$ and $(x_2,y_2)$ from the data related to years and spending amounts. If we consider year 1 as $x_1 = 1$ with $y_1=45$ and year 2 as $x_2 = 2$ with $y_2 = 54.4$.

Step2: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $x_1 = 1,y_1 = 45,x_2=2,y_2 = 54.4$ into the formula: $m=\frac{54.4 - 45}{2 - 1}=\frac{9.4}{1}=9.4$.

Answer:

The slope is $9.4$. The amount spent per person on video games increases by an average rate of $\$9.4$ per year.