Question

scatter plot shows the number of years of experience, x, and the amount charged per hour, y, for each of 24 dog sitters in avon. use the scatter plot to answer the parts below. (note that you can use the graphing tools to help you approximate the line.)
scratch area (not part of answer)
(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 11 years of experience. round your prediction to the nearest hundredth.

Explanation:

Step1: Identify two points on the line

Looking at the scatter plot, we can estimate two points. Let's assume we pick (5, 10) and (20, 25) (these are approximate from the plot).

Step2: Calculate the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the points: $m = \frac{25 - 10}{20 - 5} = \frac{15}{15} = 1$. Wait, maybe better points. Let's take (6, 9) and (18, 21). Then $m = \frac{21 - 9}{18 - 6} = \frac{12}{12} = 1$. Wait, maybe the y-intercept. Let's use point-slope. Let's take a better estimate. Suppose when x=0, y=4 (intercept). Then using point (10, 14), slope m=(14-4)/(10-0)=10/10=1. So equation is $y = x + 4$? Wait, maybe my estimates are off. Alternatively, using linear regression. Let's count the points. The scatter plot has x (years) and y (amount). Let's take two clear points: (5, 10) and (20, 25). Slope m=(25-10)/(20-5)=15/15=1. Then using point (5,10), y - 10 = 1*(x - 5) → y = x + 5. Maybe. So approximate equation: $y = x + 5$ (this is a rough estimate, actual might need better).

Step3: For part (b), substitute x=11 into the equation

Using y = x + 5, when x=11, y=11 + 5=16. But if the slope was different. Wait, maybe the correct slope is around 1. Let's check another point. If x=10, y=15. Then slope (15 - 10)/(10 - 5)=1. So equation y = x + 5. Then for x=11, y=16.

Answer:

(a) $y = x + 5$ (approximate, depends on plot), (b) 16 (approximate)