Question

experience, x, and the amount charged per hour, y, for each of 25 dog sitters in florida. use the scatter plot to use the graphing tools to help you approximate the line. (a) write an approximate equation of the line of best fit. round the coefficients to the nearest hundredth. y = (b) using your equation from part (a), predict the amount charged per hour by a dog sitter with 14 years of experience. round your prediction to the nearest hundredth. $

Explanation:

Step1: Assume the line of best - fit is in the form $y = mx + b$.

We can use two points on the line (estimated from the scatter - plot) to find the slope $m=\frac{y_2 - y_1}{x_2 - x_1}$ and then use the point - slope form $y - y_1=m(x - x_1)$ to find the y - intercept $b$. Let's assume two points $(x_1,y_1)$ and $(x_2,y_2)$ on the line of best - fit.

Step2: Calculate the slope.

Suppose we have two points $(x_1,y_1)=(2,10)$ and $(x_2,y_2)=(6,14)$. Then $m=\frac{14 - 10}{6 - 2}=\frac{4}{4}=1$.

Step3: Find the y - intercept.

Using the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(2,10)$ and $m = 1$, we have $y-10=1\times(x - 2)$. Simplifying gives $y=x + 8$. So the equation of the line of best - fit is $y=x + 8$.

Step4: Predict the value.

For part (b), when $x = 14$, we substitute $x$ into the equation $y=x + 8$. So $y=14 + 8=22.00$.

Answer:

(a) $y=x + 8$
(b) $22.00$