Question

1. rate how well you understood the lesson.

question 1
what does the slope of a line of best fit represent in a scatterplot?
the predicted change in y for each increase in x
the y - value when y = 0
the steepness of the scatterplots curve
the total number of data points
question 2
a scatterplot shows hours spent practicing and score on a video game. the line of best fit is y = 3x + 40. what does the 40 represent?
the rate of improvement

Explanation:

In a scatter - plot, the line of best fit is a linear approximation of the relationship between two variables \(x\) and \(y\). The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.

For the first question:

• The slope \(m\) of the line of best fit in the equation \(y=mx + b\) represents the change in \(y\) for a unit change in \(x\). So, it is the predicted change in \(y\) for each increase in \(x\).
• The \(y\) - value when \(y = 0\) is found by solving \(0=mx + b\) for \(x\) (i.e., \(x=-\frac{b}{m}\)), which is not the slope.
• The scatter - plot is a set of points, not a curve, so the concept of the steepness of a curve does not apply here.
• The total number of data points has no relation to the slope of the line of best fit.

Answer:

For QUESTION 1: The predicted change in \(y\) for each increase in \(x\)