Question

caleb 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 caleb to sell if the days high temperature were 12°f?

Explanation:

Step1: Find the pattern of the line

The line of best fit passes through the point \((0,91)\) (y - intercept \(b = 91\)). Let's assume the line has a linear form \(y=mx + b\). To find the slope \(m\), we can use two points on the line. For example, if we assume another point (say when \(x = 2\), \(y = 90\)). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here \(x_1 = 0,y_1=91,x_2 = 2,y_2 = 90\), so \(m=\frac{90 - 91}{2-0}=-\frac{1}{2}\). The equation of the line is \(y=-\frac{1}{2}x + 91\).

Step2: Substitute \(x = 12\) into the equation

When \(x = 12\), we substitute into \(y=-\frac{1}{2}x + 91\). So \(y=-\frac{1}{2}\times12+91\). First, calculate \(-\frac{1}{2}\times12=-6\). Then \(y=-6 + 91\).

Answer:

\(85\)