SOLUTION: Time on a treadmill. After 2 minutes on a treadmill, Jenny has a heart rate of 82. After 3 minutes she has a heart rate of 86. Assume that there is a linear equation that gives her

Question 271633: Time on a treadmill. After 2 minutes on a treadmill, Jenny has a heart rate of 82. After 3 minutes she has a heart rate of 86. Assume that there is a linear equation that gives her heart rate h in terms of time on the treadmill t. Find the equation and use it to predict her heart rate after 10 minutes on the treadmill.
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
Time on a treadmill. After 2 minutes on a treadmill, Jenny has a heart rate of 82. After 3 minutes she has a heart rate of 86. Assume that there is a linear equation that gives her heart rate h in terms of time on the treadmill t. Find the equation and use it to predict her heart rate after 10 minutes on the treadmill.
From the data we know that two points on the line are (2,82) and (3,86). From these two points we can calculate the slope m:
m = (86-82)/(3-2)
m = 4/1
m = 4
In slope-intercept form our line then is:
y = m*x + b
y = 4*x + b
We still need to find b. Since the point (2,82) is on the line we know that when y = 82, x = 2. So from above we have:
y = 4*x + b
82 = 4*2 + b
82 = 8 + b
b = 74
The line then is:
y = 4x + 74
After 10 seconds then we have:
y = 4*10 + 74
y = 40 + 74
y = 114

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