Question

Given the scatter plot on the graph below. What is the slope of the line of fit

Answer 1

Hello there. To solve this question, we'll have to remember some properties about scatter plots and slope of a line.

Given the scatter plot of the data information, we have to determine the slope of the line.

For this, we could determine it numerically using the least squares method, if we knew the data (the coordinates of the points we're plotting the best fit).

In this case, we simply need to find, by inspection, two points contained in the line and use the slope formula.

Given two points (x0, y0) and (x1, y1) that a line L passes through, then the slope m of this line is given by:

`m=(y_1-y_0)/(x_1-x_0)`

By inspection, we can easily spot the points (16, 12) and (28, 20).

Plugging these coordinates in the formula, we get:

`m=(20-12)/(28-16)`

Add the numbers and simplify the fraction

`m=(8)/(12)\overset{:4}{=}(2)/(3)`

This is the slope of this line.