Graphing Linear Equations

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Presentation transcript:

Graphing Linear Equations

Chapter Sections 7.1 – The Cartesian Coordinate System and Linear Equations in Two Variables 7.2 – Graphing Linear Equations 7.3 – Slope of a Line 7.4 – Slope-Intercept and Point-Slope Forms of a Linear Equation 7.5 – Graphing Linear Inequalities 7.6 – Functions Chapter 1 Outline

Slope of a Line

Consider the points (3, 6) and (1,2). Slope The slope of a line is the ratio of the vertical change, or rise, to the horizontal change, or run, between any two selected points on the line. Consider the points (3, 6) and (1,2).

Slope (3, 6) and (1,2) This means the graph is moving up 4 and to the right 2. Horizontal Change Vertical Change

Slope Simplifying, , so m = 2 Horizontal Change Vertical Change m = 2

Positive & Negative Slopes x y x y Positive Slope Negative Slope Line rises from left to right Line falls from left to right

Every horizontal like has a slope of 0. Horizontal Lines Every horizontal like has a slope of 0. x = 2

The slope of any vertical line is undefined. Vertical Lines The slope of any vertical line is undefined. y = -4

Parallel Lines Two non-vertical lines with the same slope and different y-intercepts are parallel . Any two vertical lines are parallel to each other. m1 = m2

Perpendicular Lines -1 m1 = m2 Two lines whose slopes are negative reciprocals of each other are perpendicular lines. Any vertical line is perpendicular to any horizontal line. m1 = m2 -1