Question

where x is the temperature, in degrees fahrenheit (°f), and y is the number of people. visitors at park temperature (°f), x number of people, y 77 243 75 276 73 253 74 257 79 281 81 294 72 265 tara calculates y = 3.3x + 16.7 to be the linear model for the data. enter numbers and select a phrase to complete the sentences using tara’s linear model. the slope of the linear model represents an expected change of based on this linear model, when the temperature is 59 degrees, tara can expect people to visit the park.

Explanation:

Step1: Interpret the slope

In the linear - equation $y = mx + b$ (where $m$ is the slope and $b$ is the y - intercept), for the equation $y = 3.3x+16.7$, the slope $m = 3.3$. The slope represents the change in $y$ (number of people) for a unit change in $x$ (temperature). So, the slope of the linear model represents an expected change of 3.3 people for every 1 - degree Fahrenheit increase in temperature.

Step2: Predict the number of people

We are given the linear model $y = 3.3x + 16.7$ and we want to find $y$ when $x = 59$. Substitute $x = 59$ into the equation:
\[

$$\begin{align*} y&=3.3\times59 + 16.7\\ &=3.3\times59+16.7\\ &=194.7+16.7\\ &=211.4 \end{align*}$$

\]
Since we are talking about the number of people, we can say Tara can expect 211 people (rounding down to the nearest whole number) to visit the park.

Answer:

The slope of the linear model represents an expected change of 3.3 people for every 1 - degree Fahrenheit increase in temperature. Based on this linear model, when the temperature is 59 degrees, Tara can expect 211 people to visit the park.