Question

the scatter plot shows the number of years of experience, x, and the amount charged per hour, y, for each of 23 dog sitters in california. 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. (b) using your equation from part (a), predict the amount charged per hour by a dog sitter with 18 years of experience. round your prediction to the nearest hundredth.

Explanation:

Step1: Assume the line of best - fit equation

The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. To find the slope $m$, we can choose two points on the line of best - fit. Let's assume two points $(x_1,y_1)$ and $(x_2,y_2)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. To find the y - intercept $b$, we can substitute one of the points and the slope into the equation $y=mx + b$ and solve for $b$.

Step2: Estimate points on the line of best - fit

Let's assume two points on the line of best - fit: $(0,8)$ and $(10,14)$. Then the slope $m=\frac{14 - 8}{10-0}=\frac{6}{10}=0.6$. Substituting the point $(0,8)$ into $y = mx + b$, we get $8=0.6\times0 + b$, so $b = 8$. The equation of the line of best - fit is $y=0.6x + 8$.

Step3: Predict the amount for 18 years of experience

Substitute $x = 18$ into the equation $y=0.6x + 8$. Then $y=0.6\times18+8=10.8 + 8=18.80$.

Answer:

(a) $y = 0.60x+8.00$
(b) $18.80$