Q39. - Algebra 2

Question

Answer the question that was posed at the beginning of the lesson. How can you determine whether your blood pressure is in a normal range? 

Include the following in your answer: 

• an explanation of how to use the graph, and 
• a description of the regions that indicate high blood pressure, both systolic and diastolic.

Step-by-Step Solution

Answer

The ordered pairs (Maximum Pressure, Minimum Pressure) that lie in the yellow shaded region represent that the blood pressure is in normal range. 

The region that lies between the two horizontal lines is the region of minimum pressure also known as diastolic.

The region that lies between the two vertical lines is the region of maximum pressure also known as systolic.

The region between the vertical lines excluding the yellow shaded region (region of normal blood pressure) is the area of high blood pressure.

Step-1 – Apply the concept of graphing the inequality

The steps to graph the inequality are provided below.

1. If the inequality contains greater than or less than sign then the boundary of the line will be dashed. If the inequality contains signs of greater than or equal to or less than or equal to then the boundary of the line will be solid. 

2. Select a point (known as test point) from the plane that does not lie on the boundary on the line and substitute it in the inequality. 

3. If the inequality is true then shade the region that contains the test point otherwise shade the other region when inequality is false.

Step-2 – Interpret the data

It is provided that blood pressure is expressed as maximum pressure over minimum pressure. The graph represents the normal blood pressure for people under the age of 40.

If the range of maximum pressure is between 100 to 140mm Hg and range of minimum pressure is between 60 to 90 mm Hg then the blood pressure is in normal range.

Step-3 – Construct the inequalities

The range of maximum pressure is between 100 to 140mm Hg and range of minimum pressure is between 60 to 90 mm Hg.

Plot the Maximum pressure on x-axis and denote by variable x.

$100\le x\le 140$

Plot the Minimum pressure on y-axis and denote by variable y.

$60\le y\le 90$

The inequalities graphed are provided below.

Step-4 – Graphical interpretation

The inequality $100\le x\le 140$ is composed to two vertical lines.

The inequality $60\le y\le 90$ is composed to two horizontal lines.

The yellow shaded region is the region common to both the inequalities.

The ordered pairs that lie in shaded region represent that blood pressure is in normal range.

For example: An order pair that lie in region is $\left(120,80\right)$. This means if a person has Maximum Pressure 120 mm Hg and Minimum Pressure 80 mm Hg, the person has normal blood pressure.

Step-5 – Graphical Description

The region that lies between the two horizontal lines is the region of minimum pressure also known as diastolic.

The region that lies between the two vertical lines is the region of maximum pressure also known as systolic.

The region between the vertical lines excluding the yellow shaded region (region of normal blood pressure) is the area of high blood pressure.