Question

a scatter plot shows the number of years of experience, x, and the amount charged per hour, y, for each of 24 dog sitters in arizona. use the scatter plot to answer the parts below. (note that you can 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: Identify two points on the line of best fit

Looking at the scatter plot, we can estimate two points. Let's take (2, 8) and (20, 18) as approximate points on the line of best fit.

Step2: Calculate the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the points: $m = \frac{18 - 8}{20 - 2} = \frac{10}{18} \approx 0.56$ (rounded to nearest hundredth).

Step3: Find the y-intercept (b)

Using the point-slope form $y - y_1 = m(x - x_1)$ with (2, 8): $y - 8 = 0.56(x - 2)$. Simplifying: $y = 0.56x - 1.12 + 8 = 0.56x + 6.88$. So the equation is $y = 0.56x + 6.88$ (approximate, values may vary slightly based on point selection).

Step4: Predict for x = 14

Substitute x = 14 into the equation: $y = 0.56(14) + 6.88 = 7.84 + 6.88 = 14.72$.

Answer:

(a) $y = 0.56x + 6.88$ (values may vary slightly)
(b) 14.72