SOLUTION: The line graph describes the target Heart Rate, in beats per minute, of a person, age in years, who is exercising. The goal os to get the number of heart beats per minute, to this

Algebra ->  Linear-equations -> SOLUTION: The line graph describes the target Heart Rate, in beats per minute, of a person, age in years, who is exercising. The goal os to get the number of heart beats per minute, to this       Log On


   

Question 146134: The line graph describes the target Heart Rate, in beats per minute, of a person, age in years, who is exercising. The goal os to get the number of heart beats per minute, to this target level. Write the equation of the line, points are (30, 136) and (70, 104). What is the rate of change in the target heart rate?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope through the points and


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28104-136%29%2F%2870-30%29 Plug in y%5B2%5D=104, y%5B1%5D=136, x%5B2%5D=70, x%5B1%5D=30, ,


m=%28-32%29%2F%2870-30%29 Subtract 136 from 104 to get -32


m=%28-32%29%2F%2840%29 Subtract 30 from 70 to get 40


m=-4%2F5 Reduce


So the slope of the line that goes through the points and is m=-4%2F5


This means that the rate of change is m=-4%2F5


Now let's use the point slope formula to find the equation of the line:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-136=%28-4%2F5%29%28x-30%29 Plug in m=-4%2F5, x%5B1%5D=30, and y%5B1%5D=136


y-136=%28-4%2F5%29x%2B%28-4%2F5%29%28-30%29 Distribute


y-136=%28-4%2F5%29x%2B24 Multiply


y=%28-4%2F5%29x%2B24%2B136 Add 136 to both sides.


y=%28-4%2F5%29x%2B160 Combine like terms.


y=%28-4%2F5%29x%2B160 Simplify


So the equation that goes through the points and is y=%28-4%2F5%29x%2B160