Question

What is the equation for the linear model in the scatter plot obtained by choosing the two points closest to the line?

Coordinate grid with scatter plot and arrow showing Variable x on horizontal x-axis and Variable y on vertical y-axis. Below the graph is a frequency distribution table showing data for Variable x and Variable y.


y=−3x+57.5


y=3.5x+57.5


y=−3.5x+32.5


y=−3.5x+57.5

Answer 1

`y=-3.5x+57.5`

Explanation:

The picture of the question in the attached figure

step 1

take the two points closest to the line in the graph

(5,40) and (15,5)

find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute

`m=(5-40)/(15-5)`

`m=-3.5`

step 2

Find the equation of the line in slope intercept form

`y=mx+b`

we have

`m=-3.5\\point\ (5,40)`

substitute and solve for b

`40=-3.5(5)+b\\b=57.5`

substitute

`y=-3.5x+57.5`