Question

Use the data in the table to answer the question. Citations are "speeding tickets." You may fill in the table to help you answer the question. Original data Line of "best guess" Line of best fit Mph greater than speed limit Number of citations Outputs Residuals Outputs Residuals 5 3 7.5 6 10 10 15 5 20 6 Find the linear approximation of the data that passes through the points (5, 3) and (20, 6).

Answer 1

Answer:

Linear approximation is given by: $y = \frac{x}{5}+2$

Step-by-step explanation:

We are given the following information in the question:

Number of citations:      5      7.5      10      15       20

 Outputs Residuals:       3       6       10       5          6

We have to find the linear approximation of the data that passes through the points (5, 3) and (20, 6).

Linear approximation is given by:

The equation of line is given by:

$(y-y_1) = \displaystyle\frac{y_2-y_2}{x_2-x_1}(x-x_1)$

where, $(x_1,y_1), (x_2.y_2)$ is the point through which the line passes.

The equation of line is:

$(y-3) = \displaystyle\frac{6-3}{20-5}(x-5)\\\\15(y-3)= 3(x-5)\\15y = 3x-15+45\\15y = 3x + 30\\y = \frac{x}{5}+2$

The above equation is the required linear approximation.