Question

create an appropriate trendline for the dataset below. using the trendline, approximate the value for miles walked on the 15th day

Explanation:

Step1: Analyze the trend

Looking at the scatter - plot, we can assume a linear trendline of the form \(y = mx + b\).

Step2: Estimate two points

Let's take two approximate points from the scatter - plot. For example, assume \((0,10)\) (when \(x = 0\), \(y=10\)) and \((25,60)\) (when \(x = 25\), \(y = 60\)).
The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{60 - 10}{25-0}=\frac{50}{25}=2\)
Using the point - slope form \(y - y_1=m(x - x_1)\) with \((x_1,y_1)=(0,10)\) and \(m = 2\), the equation of the line is \(y=2x + 10\)

Step3: Substitute \(x = 15\)

When \(x = 15\), we substitute into the equation \(y=2x+10\). So \(y=2\times15 + 10\)
\(y=30 + 10\)

Answer:

40