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3.1 – Paired Data and The Rectangular Coordinate System y 2nd Quadrant 1st Quadrant x, y x, y origin y-axis x x-axis 3rd Quadrant x, y 4th Quadrant x, y 3.1 – Paired Data and The Rectangular Coordinate System Coordinates of points: x, y Also referred as an ordered pair. The x coordinate is always first and the y coordinate is always second. Each point in the rectangular coordinate system has a unique set of coordinates. 3,0 4, 1 2,3 4, 1 2,3 3,0 3.1 – Paired Data and The Rectangular Coordinate System Graphing Equations y 2 x x y 3,6 -3 0, 0 0 2 Y X -4 3.1 – Paired Data and The Rectangular Coordinate System Graphing Equations Y x y -6 -2 3 6 X 3.1 – Paired Data and The Rectangular Coordinate System Graphing Equations and Vertical Translations Y X 3.1 – Paired Data and The Rectangular Coordinate System Graphing Equations and Vertical Translations Y X 3.1 – Paired Data and The Rectangular Coordinate System Identifying Intercepts Y 0,3 Y Y-intercept X-intercept X-intercept 2, 0 4, 0 X Y-intercept 0, 2 X 3.1 – Paired Data and The Rectangular Coordinate System Identifying Intercepts Y Y Y-intercept 0,1 Y-intercept 0,1 3,0 X-intercept X 2,0 X-intercept X 3.1 – Paired Data and The Rectangular Coordinate System Calculating Intercepts To find the x-intercepts, set y = 0 and solve for x To find the y-intercepts, set x = 0 and solve for y 2x y 4 x-intercept: y = 0 y-intercept: x = 0 2x 0 4 2x 4 x2 2 0 y 4 y 4 2, 0 0, 4 3.1 – Paired Data and The Rectangular Coordinate System Identifying Intercepts and Graphing Equations Y 0, 4 2, 0 X 3.1 – Paired Data and The Rectangular Coordinate System Calculating Intercepts To find the x-intercepts, set y = 0 and solve for x To find the y-intercepts, set x = 0 and solve for y 2x 3 y 6 0 x-intercept: y = 0 y-intercept: x = 0 2x 3 0 6 0 2 0 3 y 6 0 3y 6 0 2x 6 0 2x 6 x3 3,0 3y 6 y2 0, 2 3.1 – Paired Data and The Rectangular Coordinate System Identifying Intercepts and Graphing Equations Y 0, 2 3,0 X 3.1 – Paired Data and The Rectangular Coordinate System Graphing Vertical and Horizontal Lines x 3 x y 3 2 3 1 3 5 Y X 3.1 – Paired Data and The Rectangular Coordinate System Graphing Vertical and Horizontal Lines x4 x y 4 5 4 0 4 3 Y X 3.1 – Paired Data and The Rectangular Coordinate System Graphing Vertical and Horizontal Lines y 1 x y 4 1 1 1 3 1 Y X 3.1 – Paired Data and The Rectangular Coordinate System Graphing Vertical and Horizontal Lines y 3 x y 5 3 1 3 1 3 Y X 3.2 – The Slope of a Line Slope is a rate of change. Y x2 , y2 x1, y1 X 3.2 – The Slope of a Line Y 1,0 4,5 X 3.2 – The Slope of a Line 4,5 Y 5,1 X 3.2 – The Slope of a Line Slope of any Vertical Line x2 Y 2,3 X undefined 2, 4 3.2 – The Slope of a Line Slope of any Horizontal Line y 3 3, 3 0 Y X 4, 3 3.2 – The Slope of a Line Slopes of 5 lines are given below: Parallel Lines ( // ): two or more lines with the same slope. Which slopes represent parallel lines? 3.2 – The Slope of a Line Slopes of 5 lines are given below: The product of their slopes is –1. The slopes of perpendicular lines are negative reciprocals of each other. Which slopes represent perpendicular lines? 3.2 – The Slope of a Line What is the slope of a line that contains the following points? What is the slope of a line that is parallel to this line? What is the slope of a line that is perpendicular to this line?