RECTANGULAR COORDINATE SYSTEM

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Antony Elliott
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RECTANGULAR COORDINATE SYSTEM Quadrant II (x<0, y>0) 5 4 Quadrant I (x > 0, y>0) ORDERED PAIR: The first number in the ordered pair is the x- coordinate (aka abscissa) and the second number in the

1 RECTANGULAR COORDINATE SYSTEM Quadrant II (x<0, y>0) 5 4 Quadrant I (x > 0, y>0) ORDERED PAIR: The first number in the ordered pair is the x- coordinate (aka abscissa) and the second number in the ordered pair is the y-coordinate (aka ordinate). ( -5, 3) Origin ( 0,0 ) (, ) x-axis Quadrant III (x<0, y<0) In what Quadrant is the point (-2,-5)? (, ) y-axis Quadrant IV (x>0, y<0) (, ) What is the x-value of any point on the y-axis? What is the y-value of any point on the x-axis? A point with a negative x-coordinate is on the side of the y-axis. A point with a negative y-coordinate is on the side of the x-axis. How many units away from the x-axis is the point (0,-4)?

2 Average Rate of Change of y respect to x is Change in y / Change in x = y-value of second point y-value of first point x-value of second point x-value of first point p. 259 #34 The following table shows the mileage on and corresponding value of a used 2004 MINI Cooper, 2-door hatchback one year after it was purchased. Mileage 10, ,000 40,000 50,000 60,000 Value, in dollars 18,525 17,850 16,625 15,125 13,975 13,150 a) What was the per-mile change in the value of the car between 10,000 mi and 60,000 mi? When you see per mile, think divided by miles. Since miles in the divisor, miles must be the x-coordinate. Therefore Value of the Car is the y-coordinate. The first point is when the mileage is 10,000: (10,000, 18,525) The second point is when the mileage is 60,000: (60,000, 13,150) The per-mile change = (13,150 18,525) dollars / (60,000-10,000) miles = (-5375) dollars / (50,000) miles = dollars/mile - $0.11 per mile b) Explain the meaning of the answer to part a). The MINI Cooper LOSES 11 cents in value for each mile driven.

Example of Real World graphs The following graph has two sets of data overlaying each other. One is a scattered diagram with connected dots. The other is a bar graph.

3 Example of Real World graphs The following graph has two sets of data overlaying each other. One is a scattered diagram with connected dots. The other is a bar graph. They both share the same x-values, which in this case are levels of education. The y-values for the bar graph (Median Weekly Earnings) are on the left, since earnings is represented by dollars. The y- values for the scattered diagram (Unemployment Rates) are on the right, sinc eunemployment rates are respented as percentages. A sample data point would as follows: People with an Associate Degree have a median weekly earnings of about $700 and about a 3% unemployment rate.

5 Sometimes a set of points in a scatter diagram represents a straight line. In this case, the points represent a linear equation. A linear equation can be written in the form y = mx + b y and x are the two variables in the equation, and m and b are constants that represent the slope and y-intercept. The y-intercept is the point (0,b) where the line crosses the y-axis. Example y = ⅔ x 1 The slope, m, is ⅔ b = -1, so the y-intercept is (0,-1). All points (x,y) that lie on the line y=⅔ x -1 are values of x and y that make the equation true. Is the point (-2,-2) a solution of y=⅔ x 1? Let x = -2 and y=-2 Does -2 = ⅔(-2) 1?

6 Example 2 Find the ordered pair solution of y = ⅔ x -1 that corresponds to x = 3. The ordered-pair solution is the point (x,y) where x = 3, and y is the value of the equation y = ⅔ x -1 when x=3. y = ⅔ (3) 1 y =2-1 y = 1 Answer: The ordered pair solution of y = ⅔ x -1 that corresponds to x = 3 is (3,1) You try this one: Find the ordered-pair solution of y = -¼ x + 1 that corresponds to x=4.

7 Graph -2x + 3y = 6 Get y by itself first. Add 2x to both sides 3y = 2x + 6 Now divide both sides by 3 y = ⅔ x + 2 This tells me that the y-intercept is (0,2) and the slope is ⅔ Start at (0,2) and then go UP 2 units then RIGHT 3 units. right 3 up 2 y-intercept (0,2)

8 Graph 3x + y = 1 Get y by itself first. Subtract 3x from both sides y = -3x + 1 This tells me that the y-intercept is (0,1) and the slope is -3 A slope -3 could be written as -3/1 or 3/-1 Which means could draw our line two different ways but get the same slant. Using slope=-3/1 Start at (0,1) and then go DOWN 3 units then RIGHT 1 unit. Alternatively, we could use slope = 3/-1: Start at (0,1) and then go UP 3 units and then LEFT 1 unit. left 1 down 3 up 3 y-intercept (0,1) right 1

9 The x-intercept of a linear equation is the point on the line that crosses the x-axis. At this point y=0. The x-intercept will be an ordered pair (, 0) The y-intercept of a linear equation is the point on the line that crosses the y-axis. At this point x=0. The y-intercept will be an ordered pair (0, ) For example, find the x-intercept and y-intercept of the equation 3x + 4y = 12 The x-intercept is found by setting y=0 and solving for x. 3x + 4(0) = 12 3x = 12 x = 4 The x-intercept is (4,0) The y-intercept if found by setting x=0 and solving for y. 3(0) + 4y = 12 4y = 12 y=3 The y-intercept is (0,3) This linear equation can easily be graphed because we now have two points on the line.

Math 154 :: Elementary Algebra

Math 154 :: Elementary Algebra Math :: Elementary Algebra Section. Section. Section. Section. Section. Math :: Elementary Algebra Section. The Rectangular (Cartesian) Coordinate System. The variable x usually represents the independent