Quadrant II (x 0) Quadrant I (x > 0, y>0) ( -5, 3) x-axis Origin ( 0,0 ) Quadrant IV (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). Quadrant III (x<0, y<0) y-axis RECTANGULAR COORDINATE SYSTEM (, ) In what Quadrant is the point (-2,-5)? 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)? _________ (, )

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 right, since earnings is represented by dollars. The y-values for the scattered diagram (Unemployment Rates) are on the left, since unemployment rates are represented as percentages. A sample data point would as follows: For someone with a Bachelor’s Degree, the median weekly earnings are $1,108 and the unemployment rate is 4%.

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 slope-intercept 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. The slope represents the ratio of rise to run (rise/run) from any point on the line to another point on the line. 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 ?

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.

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 The slope is the rise/run. You can graph the line by starting at the y-intercept and using the slope to plot another point on the line. Start at (0,2) and then go UP 2 units then RIGHT 3 units. y-intercept (0,2) up 2 right 3

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. y-intercept (0,1) up 3 left 1 down 3 right 1

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.