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Graphs and Functions

Learn how to translate graphs and find slopes of linear functions in this chapter. Explore the slope-intercept form and its applications. Understand the algebra of functions and graphing linear inequalities.

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Graphs and Functions

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  1. Chapter 3 Graphs and Functions

  2. Chapter Sections 3.1 – Graphs 3.2 – Functions 3.3 – Linear Functions: Graphs and Applications 3.4 – The Slope-Intercept Form of a Linear Equation 3.5 – The Point-Slope Form of a Linear Equation 3.6 – The Algebra of Functions 3.7 – Graphing Linear Inequalities

  3. The Slope-Intercept Form of a Linear Equation § 3.4

  4. Understand Translations of Graphs y = 2x + 3 y = 2x y = 2x – 3 The lines of the graphs of these lines are parallel. We say that the graphs of these equations are vertical translations.

  5. Find the Slope of a Line The slope of a line, m,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 (1,2) and (3, 6)

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

  7. Simplifying, , so m = 2 Vertical Change Horizontal Change m = 2 Find the Slope of the Line

  8. Find the Slope of the Line Slope of a Line Through the Points (x1, y1) and (x2, y2) Example Find the slope of the line with points (-2, 3) and (1, -4).

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

  10. y = 2 Horizontal Lines Every horizontal line has a slope of 0.

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

  12. slope y-intercept y-intercept is (0, -6) slope is 3 y-intercept is (0, 3/2 ) slope is 1/2 Slope-Intercept Form In the slope-intercept form, the graph of a linear equation will always be a straight line in the form y = mx+ bwere m is the slope of the line and b is the y-intercept (0, b). y = mx+ b Examples: y = 3x– 6

  13. Slope-Intercept Form Example Write the equation -5x + 2y = 8 in slope-intercept form. The slope is 5/2; the y-intercept is (0, 4).

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