Question

flower sales
a) graph the data on the scatter plot and draw a line of best fit for the data.
b) write an equation for the line of best fit for this data.
let x represent the years since 2007 and y represent the
sales, in thousands of dollars.
c) according to your equation, in what year will the
sales reach about $400 (in thousands)? use
mathematics to explain how you determined the
answer

Explanation:

Step1: Find two points on the line of best fit

We can take two points from the data. Let's take \((x_1,y_1)=(0,305)\) (corresponding to 2007) and \((x_2,y_2)=(5,420)\) (corresponding to 2012).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the values: \(m=\frac{420 - 305}{5-0}=\frac{115}{5} = 23\).

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((0,305)\) and \(m = 23\), the point - slope form \(y-305=23(x - 0)\).

Step4: Simplify the equation

Simplifying \(y-305=23x\) gives \(y = 23x+305\).

Answer:

\(y = 23x + 305\)