Part 2 The data in table 2 below represent the maximum benefit to the heart from
ID: 3037630 • Letter: P
Question
Part 2
The data in table 2 below represent the maximum benefit to the heart from exercising, if the heart rate is in the target heart rate zone. In the table, x represents different age groups and y represents the number of heart beats per minute.
Table 2: Maximum benefit to the heart from exercising
Age, x
Maximum number of heart beats, y
20
140
30
133
40
126
50
119
60
112
70
105
Select any two points and find an equation of the line containing the two points.
(40, 126) and (50, 119)
1-interpret the slope of the line found above. How do you explain that particular negative value of the slope?
2-Calculate the slope for every pair of points. If the slopes are the same, determine whether the relation is linear or not.
3-Does the relationship defined by the set of ordered pairs (x, y) represent a function? If yes, write the domain and range. Re-write the equation using function notation.
4-Use the above function to predict the maximum number of heart beats for ages of 25, 55, 65 and 80.
5-Using the above function, what is the approximate age of a person whose maximum number of heart beats is 115?
Age, x
Maximum number of heart beats, y
20
140
30
133
40
126
50
119
60
112
70
105
Explanation / Answer
Let the equation of the line containing the points (40, 126) and (50, 119) be y = mx +c, where m is the slope of the line and c is its y-intercept. Then m = (119-126)/(50-40) = -7/10. Then the equation of the line changes to y =-7x/10+c. Now, on substituting x = 50 and y = 119 in this equation, we get 119 = -(7*50)/10 +c or, c-35 = 119 so that c = 119+35 = 154. Hence the equation of the required line is y = -7x/10+154.
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