The average systolic blood pressure for a 26yearold is 113 a

The average systolic blood pressure for a 26-year-old is 113 and for 40-year-old is 120. a) Determine a linear function in slope/y-intercept form that models the systolic blood pressure P(x) for a x-year-old individual. b)What does the slope represent in terms of blood pressure and age?

Solution

a) Let the linear function in slope/y-intercept form that models the systolic blood pressure P(x) for a x-year-old individual be y = mx + c, where m is the slope and c is the y-intercept. Now, since y = 113 when x = 26, on substituting these values of x and y in the equation, we get 113 = 26m +c ...(1). Also, when x = 40, y = 120; on substituting these values of x and y in the equation, we get  120 = 40m +c...(2). On subtracting the 1st equation from the 2nd equation, we get 40m+ c -26m - c = 120 - 113 or, 14m = 7. Therefore, m = 7/14 = 1/2. On substituting m = 1/2 in the 1st equation, we get (26*1/2 + c = 113 or, 13 + c = 113. Therefore, c = 113 -13 = 100.

Then the equation of the required linear function is y = x/2 + 100.

b) The slope represents that the average systolic blood pressure goes up as the age increases.