Section 1
Rectangular Coordinate System
a. In a rectangular coordinate system, two number lines are drawn at right angles to each other. The horizontal line is called the _________-axis, and the vertical line is called the _______.b. A point in a rectangular coordinate system is defined by an ________ pair, $(x, y)$c. In a rectangular coordinate system, the point where the $x$ - and $y$ -axes intersect is called the _______ and is represented by the ordered pair _______.d. The $x$ - and $y$ -axes divide the coordinate plane into four regions called _____.e. A point with a positive $x$ -coordinate and a ________ $y$ -coordinate is in Quadrant IV.In Quadrant ________ both the $x$ - and $y$ -coordinates are negative.
b. A point in a rectangular coordinate system is defined by an_________pair, $(x, y)$
The number of Botox $^{@}$ injection procedures (in millions) in the United States over a 6-year period is shown in the graph.a. For which year was the number of procedures the greatest?b. Approximately how many procedures were performed in year $5 ?$c. Which year corresponds to 2.3 million procedures?
The number of patients served by a certain hospice care center for the first 12 months after it opened is shown in the graph.a. For which month was the number of patients greatest?b. How many patients did the center serve in the first month?c. Between which months did the number of patients decrease?d. Between which two months did the number of patients remain the same?e. Which month corresponds to 40 patients served?f. Approximately how many patients were served during the 10 th month?
Recently the number of housing permits (in thousands) issued by a county in Texas between year 0 and year 6 is shown in the graph.a. For which year was the number of permits greatest?b. How many permits did the county issue in year $0 ?$c. Between which years did the number of permits decrease?d. Between which two years did the number of permits remain the same?e. Which year corresponds to 7000 permits issued?
The price per share of a stock (in dollars) over a period of 5 days is shown in the graph.a. Interpret the meaning of the ordered pair (1,89.25) .b. What was the change in price between day 3 and day $4 ?$c. What was the change in price between day 4 and day $5 ?$
The price per share of a stock (in dollars) over a period of 5 days is shown in the graph.a. Interpret the meaning of the ordered pair (1,10.125) .b. What was the change between day 4 and day $5 ?$c. What is the change between day 1 and day $5 ?$
Plot the points on a rectangular coordinate system.a. (2,6)b. (6,2)c. (-7,3)d. (-7,-3)e. (0,-3)f. (-3,0)g. (6,-4)h. (0,5)
Plot the points on a rectangular coordinate system.a. (4,5)b. (-4,5)c. (-6,0)d. (6,0)e. (4,-5)f. (-4,-5)g. (0,-2)h. (0,0)
Plot the points on a rectangular coordinate system.a. (-1,5)b. (0,4)c. $\left(-2,-\frac{3}{2}\right)$d. (2,-1.75)e. (4,2)f. (-6,0)
Plot the points on a rectangular coordinate system.a. (7,0)b. (-3,-2)c. $\left(6 \frac{3}{5}, 1\right)$d. (0,1.5)e. $\left(\frac{7}{2},-4\right)$f. $\left(-\frac{7}{2}, 4\right)$
Identify the quadrant in which the given point is located.$$\text { identify the quadrant in which the given point is located. }$$
Identify the quadrant in which the given point is located.$$(25,16)$$
Identify the quadrant in which the given point is located.$$(-8,14)$$
Identify the quadrant in which the given point is located.$$(-82,-71)$$
Identify the quadrant in which the given point is located.$$(-5,-19)$$
Identify the quadrant in which the given point is located.$$(-31,6)$$
Identify the quadrant in which the given point is located.$$\left(\frac{5}{2}, \frac{7}{4}\right)$$
Identify the quadrant in which the given point is located.$$(9,-40)$$
Explain why the point (0,-5) is not located in Quadrant IV.
Explain why the point (-1,0) is not located in Quadrant II.
Where is the point $\left(\frac{7}{8}, 0\right)$ located?
Where is the point $\left(0, \frac{6}{5}\right)$ located?
Refer to the graph.Estimate the coordinates of the points $A, B, C, D, E,$ and $F$.
Refer to the graph.Estimate the coordinates of the points $G, H, I, J, K,$ and $L$
A map of a park is laid out with the visitor center located at the origin. Five visitors are in the park located at points $A, B, C, D,$ and $E$. All distances are in meters.a. Estimate the coordinates of each visitor.b. How far apart are visitors $C$ and $D ?$
A townhouse has a sprinkler system in the backyard. With the water source at the origin, the sprinkler heads are located at points $A, B, C, D,$ and $E .$ All distances are in feet.a. Estimate the coordinates of each sprinkler head.b. How far is the distance from sprinkler head $B$ to $C ?$
The age and systolic blood pressure (in millimeters of mercury, $\mathrm{mm} \mathrm{Hg}$ ) for eight different women are given in the tablea. Write the corresponding ordered pairs using the woman's age as the $x$ -variable and the systolic blood pressure as the $y$ -variable. Interpret the meaning of the first ordered pair.b. Plot the data points on a rectangular coordinate system.
The following table shows the average temperature in degrees Celsius for Montreal, Quebec, Canada, by month.a. Write the corresponding ordered pairs, letting $x=1$ correspond to the month of January.b. Plot the ordered pairs on a rectangular coordinate system.
The table shows the average temperature in degrees Fahrenheit for Fairbanks, Alaska, by month.a. Write the corresponding ordered pairs, letting $x=1$ correspond to the month of January.b. Plot the ordered pairs on a rectangular coordinate system.
The data in the table give the percent of males and females who have completed 4 or more years of college education for selected years. Let $x$ represent the number of years since $1960 .$ Let $y$ represent the percent of men and the percent of women that completed 4 or more years of college.$$\begin{array}{c|c|c|c}\text { Year } & x & \begin{array}{c}\text { Percent, } y \\\text { Men }\end{array} & \begin{array}{c}\text { Percent, } y \\\text { Women }\end{array} \\\hline 1960 & 0 & 9.7 & 5.8 \\\hline 1970 & 10 & 13.5 & 8.1 \\\hline 1980 & 20 & 20.1 & 12.8 \\\hline 1990 & 30 & 24.4 & 18.4 \\\hline 2000 & 40 & 27.8 & 23.6 \\\hline 2005 & 45 & 28.9 & 26.5 \\\hline 2010 & 50 & 29.9 & 28.8 \\\hline\end{array}$$a. Plot the data points for men and for women on the same graph.b. Is the percentage of men with 4 or more years of college increasing or decreasing?c. Is the percentage of women with 4 or more years of college increasing or decreasing?
Use the data and graph from Exercise 31 to answer the questions.a. In which year was the difference in percentages between men and women with 4 or more years of college the greatest?b. In which year was the difference in percentages between men and women the least?c. If the trend continues beyond the data in the graph, does it seem possible that in the future, the percentage of women with 4 or more years of college will be greater than or equal to the percentage of men?