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Question 70228: after 2 minutes on a treadmill jenny has a heart raete of 84. after 3 minutes she has a heart rate of 86. assume that there is a linear equation that gives her heart rate h in the terms of time on the treadmill t. Find the equation and use it to find her heart rate after 10 minutes on the treadmill
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! One approach to solving this problem is to treat the given input data, ie, heart-rate and time, as the coordinates of points on a graph. Instead of the usual (x, y) you can use (t, h) where t is time and h is heart rate.
With the two given points you can find the slope of this linear relationship using:
 or rather: 
Once you have found the slope, you can start writing the equation in the slope-intercept form (h = mt+b) which will be just perfect for this problem.
Let's find the slope using the two given point (t, h) which are: (2, 84) and (3, 86)
You can now write the start of the equation as:
 where b is the h-intercept. Substitute the t- and h-coordinates from either one of the two given points and solve for b. Using (2, 84) we get:
 Simplify and solve for b.
Now you can write the final equation for this linear relationship:
To find Jenny's heart rate (h) after 10 minutes (t=10) on the treadmill, make the appropriate substitutions into your final equation and solve for h.
Jenny's heart rate will be 100 bpm after 10 minutes on the treadmill.
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