Question

two students have examined the scatter plot shown and have created a line of best fit for the data . student a believes that the line of best fit for the data is y=-2x+24, wow student B believes that the line of the best fit for the data is y =1.5x+23. determine which student created a better line of best fit given the data in the graph. justify your answer using mathematics

Answer 1

Pick any two points on the graph

We use the points (0,23) and (5,14)

`\begin{gathered} \text{Slope}=\frac{Change\text{ in y}}{\text{Change in x}} \\ =(14-23)/(5-0) \\ =-(9)/(5) \\ =-1.8 \end{gathered}`

Since the slope is negative, we conclude that the line of best fit is:

`y=-2x+24`

Since the other line y=1.5x+24 has a positive slope.