Question

1. the scatter plot shows the weight of a person, y, and the week into their diet, x.

a) find the line of best fit for the data.
b) predict the person’s weight after 12 weeks.

Explanation:

Step1: Identify Points

From the scatter plot, let's list the coordinates \((x, y)\) where \(x\) is weeks and \(y\) is weight. Estimating from the grid:

• \(x = 0, y = 160\)
• \(x = 1, y \approx 155\)
• \(x = 2, y \approx 152\)
• \(x = 3, y = 150\)
• \(x = 4, y = 150\)
• \(x = 5, y \approx 148\)
• \(x = 6, y \approx 145\)
• \(x = 7, y \approx 142\)
• \(x = 8, y \approx 140\)

Step2: Calculate Line of Best Fit (Slope and Intercept)

The general form is \(y = mx + b\), where \(m\) is slope and \(b\) is y-intercept.

• Slope (\(m\)): Use two points, e.g., \((0, 160)\) and \((8, 140)\).

\(m=\frac{140 - 160}{8 - 0}=\frac{-20}{8}=-2.5\)

• Y-intercept (\(b\)): At \(x = 0\), \(y = 160\), so \(b = 160\).

Thus, the line of best fit is \(y=-2.5x + 160\).

Step3: Predict at \(x = 12\)

Substitute \(x = 12\) into \(y=-2.5x + 160\):
\(y=-2.5(12)+160=-30 + 160 = 130\).

Answer:

a) The line of best fit is \(y = -2.5x + 160\) (or similar based on point estimation).
b) The predicted weight after 12 weeks is \(\boldsymbol{130}\) (units of weight, e.g., pounds/kg).