Question

the scatter plot denotes the relationship between the months worked at a company and the employees hourly wage. what is the equation of the line of best fit? question 8 (1 point) using the equation that you found in question 7, predict how many months it would take to earn an hourly wage of $40.

Explanation:

Step1: Analyze the slope - positive trend

The scatter - plot shows a positive relationship between months worked ($x$) and hourly wage ($y$), so the slope of the line of best - fit should be positive. This eliminates the options with negative slopes: $y=-0.25x + 9.25$ and $y=-4x - 17$.

Step2: Estimate slope and y - intercept

We can estimate the slope by choosing two points on the line of best - fit. Let's assume the line passes through approximately $(2,9.75)$ and $(6,10.75)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{10.75 - 9.75}{6 - 2}=\frac{1}{4}=0.25$. The y - intercept can be estimated by looking at where the line crosses the y - axis. It seems to cross around $y = 9.25$. So the equation of the line of best - fit is $y = 0.25x+9.25$.

Step3: Solve for $x$ in Question 8

We use the equation $y = 0.25x+9.25$ from the previous step. We want to find $x$ when $y = 40$. Substitute $y = 40$ into the equation:
\[

$$\begin{align*} 40&=0.25x + 9.25\\ 40-9.25&=0.25x\\ 30.75&=0.25x\\ x&=\frac{30.75}{0.25}=123 \end{align*}$$

\]

Answer:

Question 7: A. $y = 0.25x + 9.25$
Question 8: 123 months