Question

Kelsey cut a watermelon into pieces. She takes 10 of the pieces and counts the number of white tees and the number of black seeds in each piece. The scarlet plots below represent her data and a line of best fit. Based on the line of best fit, how many white seeds should Kelsey expect in a piece of watermelon that has 90 black seeds?

Answer 1

The equation of a line passing through two points is given by,

`y-y_1=(y_2-y_1)/(x_2-x_1)*(x-x_1)`

Consider that the line of best fit passes through (9,5) and (12,6),

`\begin{gathered} y-5=(6-5)/(12-9)*(x-9) \\ y-5=(1)/(3)*(x-9_{}) \\ 3y-15=x-9 \\ x-3y+6=0 \end{gathered}`

Note that 'x' denotes the number of black seeds, and 'y' denotes the number of white seeds in a particular piece of watermelon.

The value of 'y' corresponding to 90 black seeds i.e. x=90, is calculated as,

`\begin{gathered} 90-3y+6=0 \\ 3y=96 \\ y=32 \end{gathered}`

Thus, Kelsey should expect 32 white seeds in a piece of watermelon that has 90 black seeds.