SOLUTION: 10.)The horsepower produced by an automobile engine was recorded for various engine speeds in the range of 2,400 to 4,800 revolutions per minute (rpm). The data were recorded on th

Algebra ->  Graphs -> SOLUTION: 10.)The horsepower produced by an automobile engine was recorded for various engine speeds in the range of 2,400 to 4,800 revolutions per minute (rpm). The data were recorded on th      Log On


   



Question 938702: 10.)The horsepower produced by an automobile engine was recorded for various engine speeds in the range of 2,400 to 4,800 revolutions per minute (rpm). The data were recorded on the following scatter diagram. Find an equation of the line that models the relationship between engine speed s and horsepower h. Write the equation in slope-intercept form
http://www.webassign.net/waplots/b/c/daf612685275b6fe720471eb19d923.gif

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
If you look carefully at the points and the line, you will see that
there are two points that are exactly on the line.

They are (3600,230) and (4000,260)

We will use x for engine speed and h for horsepower since your
graph has horizontal axis as engine speed and vertical axis as
horsepower.  At the end we'll switch to the letters s and h.

So we use the slope formula and the point-slope formula.

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m+=%28260-230%29%2F%284000-3600%29+=+30%2F400+=+0.075

The we substitute in the point-slope formula for the equation
of a line:

y-y%5B1%5D=m%28x-x%5B1%5D%29

y-230=0.075%28x-3600%29

y-230=0.075x-270

y=0.075x-40  <-- slope-intercept form y=mx+b

Finally, since y represents horsepower, we replace y by h and since
x represents engine speed, our final equation is

h+=+0.075s-40 

Edwin