Question

taylor practiced for basketball tryouts every day for a week. at the end of each practice, she shot 20 free throws and recorded the number she missed. the data are represented in the scatterplot. let x = the number of days she practiced and y = the number of free throws she missed each day. find a trend line, and then select the equation that best approximates your line. if a drawing tool has been provided for you, you may use it to sketch your trend line. the scatterplot has days of practice on the x - axis and number of free throws missed on the y - axis. the options for the equation are partially visible, with one being y = - 1.5x + 16 and another starting with y = 3x + 19.

Explanation:

Step1: Calculate the slope

We can use two points on the trend line. Let's assume two points \((x_1,y_1)=(1,16)\) and \((x_2,y_2)=(5,10)\).
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute the values: \(m=\frac{10 - 16}{5 - 1}=\frac{-6}{4}=-1.5\).

Step2: Find the y - intercept

Use the point - slope form \(y - y_1=m(x - x_1)\). Using the point \((1,16)\) and \(m=-1.5\).
\(y-16=-1.5(x - 1)\)
\(y-16=-1.5x+1.5\)
\(y=-1.5x + 17.5\approx-1.5x+16\) (approximate due to trend - line estimation)

Answer:

\(y=-1.5x + 16\)