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Rectangular Coordinate System

Rectangular Coordinate System. In pre-algebra, we used number lines to plot numbers and equations and inequalities of 1 variable (x = -3, x < 4 => one-dimensional). -5. -4. -3. -2. -1. 1. 2. 3. 4. 5. 0.

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Rectangular Coordinate System

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  1. Rectangular Coordinate System • In pre-algebra, we used number lines to plot numbers and equations and inequalities of 1 variable (x = -3, x < 4 => one-dimensional) -5 -4 -3 -2 -1 1 2 3 4 5 0 • To examine equations involving 2 variables, we graph on a rectangular (Cartesian) coordinate system (y = x, y = x - 1 => two-dimensional) • On a plane, each point is a pair of numbers => (1,2); (-2,-3); (3,-1) 4 4 3 3 (1,2) 2 2 origin (0,0) 1 1 x - axis -4 -3 -2 -1 1 2 3 4 -4 -3 -2 -1 1 2 3 4 -1 -1 (3,-1) -2 -2 y - axis -3 -3 (-2,-3) -4 -4

  2. Quadrants and Finding Coordinates • Coordinates like (2,3) are called ordered pairs and are of the form (x,y), where x is the x-coordinate, and y is the y-coordinate • Graphs can be divided into 4 quadrants • Quadrant I => both coordinates are positive • Quadrant II => 1st-coordinate negative / 2nd-coordinate positive • Quadrant III => both coordinates are negative • Quadrant IV => 1st-coordinate positive / 2nd-coordinate negative Bonus: Plot the points (-1,-3) , (3/2,5/2) , and (3,4) R: ( , ) B: ( , ) G: ( , ) P: ( , ) 4 4 3 3 I II 2 2 1 1 -4 -3 -2 -1 1 2 3 4 -4 -3 -2 -1 1 2 3 4 -1 -1 III -2 IV -2 -3 -3 -4 -4

  3. Solutions of Equations • To determine if an ordered pair is a solution of an equation, we use the 1st number in the pair to replace the variable that occurs 1stalphabetically • The solution of an equation in 2 variables (typically x and y) is an ordered pair which when substituted into the equation give a true statement • Because of this, we can generate ordered-pair solutions to equations to graph • Substituting x = 2 into y = 3 – x2 gives an ordered pair solution of (2, ) • Show that (-2,-1) is a solution to y = 3 – x2 • Graph y = 3 – x2 by using numbers from -2 to 2 for x and finding the coordinates 4 3 2 1 -4 -3 -2 -1 1 2 3 4 -1 -2 • Graph y = |x| and y = 2x – 1 on the board with time -3 -4

  4. Identifying Intercepts • A y-intercept of a graph is a point where the graph intersects the y-axis (this is also the point where x = 0) • An x-intercept of a graph is a point where the graph intersects the x-axis (this is also the point where y = 0) • Two graphs intersect each other at any point where their x-coordinates and y-coordinates are the same • Find the x and y intercepts for the following… 6 5 Red: Blue: Green: Purple: 2x + 5y = 10: y = 4 – x2: 4 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 -5 • Bonus: At what points do the blue and green graph intersect each other? -6

  5. Interpreting Graphs Book problems: 1, 3, 5, 9, 11, 13, 17, 23, 39, 45, 57 • Line graphs are often used to show trends over time or a range • By identifying points on line graphs and their coordinates, you can interpret specific information given in the graph • How many rushing yards did the Hokies have in 2006? In 2009? • How many passing yards did the Hokies have in 2003? • For the period given, what is the biggest total of rushing yards in a season for the Hokies and in what season? • Around how many more passing yards did VT have than rushing yards in 2008? • How many more yards passing did the Hokies have in 2011 than the previous season (y)?

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