Question

Irma is an arborist, or a person who specializes in caring for trees. This scatter plot shows the ages and heights of the maple trees at the nursery where she works. It also shows the line of best fit.

Answer 1

What would you like to do with the plot — interpret it, find the equation of the line of best fit, or make predictions from it? I can help any of those.

If you want the equation of the line and predictions, here are the steps I’ll follow (and you can paste the coordinates or two clear points from the line if you want me to compute it exactly):

1. Pick two points that lie on the line of best fit (use points where the line crosses grid intersections for accuracy).
2. Compute the slope: m = (change in height) / (change in age) = (y2 − y1) / (x2 − x1). Units will be height per year (e.g., feet/year or cm/year).
3. Find the y-intercept b by substituting one point into y = mx + b, so b = y − m x.
4. The line is y = m x + b. Use that to predict height for any age x (but be careful about extrapolating far beyond the observed ages).
5. Interpret: m tells you how much taller a tree gets per year on average; b is the model’s predicted height at age 0 (often not literally meaningful). Also note how tightly the points cluster around the line to judge how good the fit is.

If you paste two grid points on the best-fit line (or the plotted data points), I’ll compute the equation and any predictions you want.