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Objective

Learn how to graph linear equations in slope-intercept form and graph linear inequalities using different methods. Understand parallel and perpendicular lines. Practice graphing linear equations and inequalities.

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Objective

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Presentation Transcript

  1. Objective • I will graph linear equations in slope-intercept form. • I will graph linear inequalities using one of the three methods of graphing.

  2. Slope-Intercept Form of the Equation of a Line • A linear equation written in the form of y = mx + b • m = slope • b = y-intercept

  3. Graphing Using Slope and Y-intercept Graph the equation -2x + y = 3. -2x + y = 3 Original Equation y = 2x + 3 Write equation in slope-intercept form Slope: m = 2 Y-intercept: b = 3 • Plot the y-intercept (0, 3) • Draw a slope triangle to find a second point • m = 2(Rise)/1(Run) • Connect the points

  4. Guided Practice • Graph the equation using slope-intercept form. 1. 6x - y = 1

  5. Parallel Lines • Two different lines in the same plane that do not intersect • m1 = m2 • To find, write in slope-intercept form

  6. Identifying Parallel Lines • Which of the following lines are parallel. line a: -2x + y = 4 line b: 2y = -4x + 6 line c: 4y = 8x - 4

  7. Perpendicular Lines • Two different lines in the same plane that intersect at a right (90º) angle • The slopes of the perpendicular lines are negative reciprocals • m1 • m2 = -1 • To find, write equation in slope-intercept form, then multiply slope by negative reciprocal

  8. Finding a Perpendicular Line • Find the slope of the line perpendicular to 2y = 6x + 8. 2y = 6x + 8 y = 3x + 4 Slope-Intercept Form m1 = 3

  9. Guided Practice 1. Find the slope of the line parallel and perpendicular to the following line. 2x + 4y = 12

  10. Graphing Linear Inequalities • Use one of the three methods learned for graphing linear equations (table, intercepts, or slope-intercept form) • < - use a dotted line and shade below line • > - use a dotted line and shade above line • ≤ - use a solid line and shade above line • ≥ - use a solid line and shade above line

  11. Graphing Linear Inequalities • Graph -2x + y > 3 -2x + y > 3 y > 2x + 3 Slope-Intercept Form m = 2, b = 3 Graph

  12. Guided Practice 1. Graph 2y ≥ -6x + 4.

  13. Independent Practice • Graph the equation using slope-intercept form. 3x - y = 4 • Find the slope of the line parallel and perpendicular to the given line. 4x + 3y = 9 3. Graph 4y > 5x - 8.

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