The Equation of a Line 1 Assignment | Assignment Help Services

As part of the second stage of a drug trial, volunteers are given one of two dosages, in order to determine therapeutic levels. Volunteers who were given 6.5 mg had blood concentrations of 2.7 parts per million (ppm), while volunteers who were given 10 mg had blood concentrations of 5.1 ppm.

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a.) Determine the equation of a line that models this data, where x is the dosage given and y is the blood concentration.

The equation of line 1

points: (x, y) = (6.5, 2.7) and (10, 5.1)

Use the point slope equation

y – 2.7 = 5.1 – 2.7 / 10 – 6.5

y = 24/35 (x – 6.5) + 2.7

y = 24/35 x – 123/70

Graph this line. (I already have the line graphed)

c. If the desired concentration in the bloodstream is 7.5 ppm, what should be the therapeutic dosage?

y = 7.5

24/35 x – 123/70 = 7.5

⇒24x/35 = 7.5 + 123/70

⇒ x = 324/35 * 35/24

⇒ x = 13.5mg     (Now I need the therapeutic dosage.)

d. If the toxic concentration in the bloodstream is 11.8 ppm, what is the maximum safe dosage?

y = 11.8

⇒ 24/35 x – 123/70 = 11.8

⇒ 24x/35 = 949/70

⇒ x = 949/70 * 35/24

x = 19.77mg  (I need the maximum safe dosage as well.)

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