t(min)x-value:36,38,40,42,44
heartbeats-y value: 2530, 2661, 2806,2948,3080
Graph these points(Each point goes with another so (36,2530), (38,2661)...
The monitor estimates this value by calculating the slope of a secant line. Use the data to estimate the heart rate after 42 minutes using the secant line between the points with the given values of t.
they give me t=36 and t=42 for the first problem:
First I found the slope between both points which i got 69.67.
then after i convert it to y=mx+b form. Then do i plug in 42 for x to find the heart rate.
Is that the right steps or no?
If the slope of the secant line is 69b/min, then x=42, m=69
Yes.
Yes, you are on the right track with your steps. Let me explain it in more detail.
To estimate the heart rate after 42 minutes using the secant line between the points at 36 minutes and 42 minutes, you need to follow these steps:
1. Calculate the slope of the secant line:
- Find the change in the y-values (heartbeats) by subtracting the heartbeats at t = 36 minutes from the heartbeats at t = 42 minutes. In this case, it is 2948 - 2530 = 418.
- Find the change in the x-values (minutes) by subtracting the value of t at 36 minutes from the value of t at 42 minutes. In this case, it is 42 - 36 = 6.
- Divide the change in y-values by the change in x-values to find the slope. In this case, it is 418 / 6 = 69.67.
2. Write the equation of the secant line in slope-intercept form (y = mx + b):
- Choose one of the given points, for example, (36, 2530), and substitute the values of x and y into the equation.
- Using the slope you calculated in step 1, replace m in the equation with the slope value.
- Solve the equation for b, the y-intercept.
3. Once you have the equation of the secant line in the form y = mx + b, plug in the x-value of 42 (minutes) into the equation and solve for y. This will give you the estimated heart rate after 42 minutes.
So, your steps are correct. By finding the slope, converting it to the y = mx + b form, and then plugging in x = 42, you will be able to estimate the heart rate after 42 minutes.