Question

The scatterplot below shows the ages of some children in the amount of time each been playing outside last week. Which equation could represent the line of best fit for the number of hours a child spends playing outside based on the age of the child? Is the correct answer A, B, C, or D?

Answer 1

y = 0.75x + 45

Step-by-step explanation:

The line of best fit is a line that describes in a better way the distribution of the points. Therefore, the best fit will be like

Then, the equation of this line can calculate using two points in the line, for example (x1, y1) = (2, 6) and (x2, y2) = (6, 9). So, the slope of the line is

`m=(y_2-y_1)/(x_2-x_1)=(9-6)/(6-2)=(3)/(4)=0.75`

Finally, the equation of the line is

`\begin{gathered} y-y_1=m(x-x_1) \\ y-6=0.75(x-2) \\ y-6=0.75x-0.75(2) \\ y-6=0.75x-1.5 \\ y=0.75x-1.5+6 \\ y=0.75x+4.5 \end{gathered}`

Therefore, the answer is

y = 0.75x + 45