When you graph the data and use a line to fit the points you get something like this:
As you can see the line goes through the second and last point, then we can find the equation of the line that best fits the data by expressing the equation of the line that goes through these points (points (946,104) and (1003,30.6)).
The equation of a line has the form:
y=mx+b
where m is the slope of the line and b its intercept
The slope of the line is given by the formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Then, by taking the points (946, 104) and (1003, 30.6), we get:
[tex]m=\frac{30.6-104}{1003-946}=-1.29[/tex]
Now that we know the slope of the line, we can use it, to replace it into the general formula of a linear equation and then solve for b, like this:
y= -1.29*x + b
By taking the point (946,104), we get:
104= -1.29*946+b
b = 104 +1.29*946 = 1322.18
Then, the equation of the line that best fits the data is:
[tex]y=-1.29x+1322.18[/tex]
