Question

dylan has a part - time job at an ice skating rink selling hot cocoa. he decided to plot the number of hot cocoas he sold relative to the days high temperature and then draw the line of best fit. based on the line of best fit, how many hot cocoas would you predict dylan to sell if the days high temperature were 25°f?

Explanation:

Step1: Find the slope of the line of best - fit

The line of best - fit passes through the points $(0,104)$ and $(10,96)$. The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1=104,x_2 = 10,y_2 = 96$. So, $m=\frac{96 - 104}{10-0}=\frac{-8}{10}=-0.8$.

Step2: Find the equation of the line of best - fit

The equation of a line in slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Since the line passes through $(0,104)$, the y - intercept $b = 104$. So the equation of the line is $y=-0.8x + 104$.

Step3: Make a prediction

We want to find the number of hot cocoas $y$ when the high temperature $x = 25$. Substitute $x = 25$ into the equation $y=-0.8x + 104$. Then $y=-0.8\times25+104$. First, calculate $-0.8\times25=-20$. Then $y=-20 + 104=84$.

Answer:

84