Question

Which equation is the best approximation of the trend line

Answer 1

approximatesThe equation of a line is given by

`\begin{gathered} y=mx+c \\ m=\frac{change\text{ in y}}{change\text{ in x}}=(y_2-y_1)/(x_2-x_1)=(y-y_1)/(x-x_1) \end{gathered}`

Taking two points from the line of best fit

Point A(14,200) and Point B (18,400)

`\begin{gathered} x_1=14;y_1=200;x_2=18;y_2=400 \\ (y_2-y_1)/(x_2-x_1)=(y-y_1)/(x-x_1) \\ (400-200)/(18-14)=(y-200)/(x-14) \\ (200)/(4)=(y-200)/(x-14) \\ (50)/(1)=(y-200)/(x-14) \\ y-200=50(x-14) \\ y-200=50x-700 \\ y=50x-700+200 \\ y=50x-500 \end{gathered}`

Hence, the equation that best approximate the trend line is y=50x-500