Question

The scatter plot below shows the profit earned each month by a new company over the first year of operation.

The owner writes a line of best fit equation, shown below, to model the relationship between profit earned and month.

y = 2,500x - 2,500

Explain how you know that the line of best fit equation is appropriate, mentioning both the slope and y-intercept in your response.

Answer 1

Step-by-step explanation:

To determine the slope and y-intercept of the equation, let us plot the coordinates in the slope-intercept form.

Analyzing the graph, some of the points that are on the straight line is (1,0),(3,5), (9,20)

Let us consider the points (1,0),(3,5) to determine the slope.

`\begin{aligned}m &=(5-0)/(3-1) \\&=(5)/(2) \\&=2.5\end{aligned}`

Since, the profit is earned in thousands of dollars, m = 2.5 or m = 2500

Thus, slope = 2500

To determine the y- intercept, let us substitute any one of the coordinate from the graph.

Thus, let us substitute (1,0) in the equation
`y=mx+b` to determine the y-intercept.

`0=2500(1)+b\\`

Simplifying, we have,

`b=-2500`

Hence, the line of best fit equation is
`y=2500x-2500`