Question

or state correctional authorities
part 1 of 3
(a) use the given points to create a linear model of the data. express numbers as decimals or integers.
the linear model in slope - intercept form is y = 41.5x + 824.
part: 1 / 3
part 2 of 3
(b) what does the slope mean in the context of this problem?
the slope means that the number of prisoners increased at a rate of per year during the given time period.

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In the model $y = 41.5x+824$, the slope $m = 41.5$.

Step2: Interpret slope in context

The $x$ - variable represents the year and the $y$ - variable represents the number of prisoners (in thousands). The slope represents the rate of change of the number of prisoners with respect to time.

Answer:

The slope means that the number of prisoners increased at a rate of 41.5 thousand per year during the given time period.