Chapter 3 Introduction to Graphing and Equations of Lines

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Presentation transcript:

Chapter 3 Introduction to Graphing and Equations of Lines Section 6 Parallel and Perpendicular Lines

Section 3.6 Objectives 1 Determine Whether Two Lines Are Parallel 2 Find the Equation of a Line Parallel to a Given Line 3 Determine Whether Two Lines Are Perpendicular 4 Find the Equation of a Line Perpendicular to a Given Line

Parallel Lines Two nonvertical lines are parallel if and only if their slopes are equal and they have different y-intercepts. Vertical lines are parallel if they have different x-intercepts. x y x y m1 = m2 m1 = m2

Parallel Lines Example: Determine whether the line 6x + 2y = 9 is parallel to – 3x – y = 3. Find the slope of each line. 6x + 2y = 9 – 3x – y = 3 The slopes are the same so the lines are parallel.

Parallel Lines Example: Find the equation of the line that is parallel to 4x + y = – 8 and contains the point (2, – 3). Write the equation in slope-intercept form. Find the slope of the line. 4x + y = – 8 y = – 4x – 8 Use the point-slope form to find the equation. Substitute in the values. Simplify. Subtract 3 from both sides.

Perpendicular Lines m1m2 =  1 or m1 = Two nonvertical lines are perpendicular if and only if the product of their slopes is – 1. Any vertical line is perpendicular to any horizontal line. x y m1m2 =  1 or The slopes are negative reciprocals of each other. m1 =

Perpendicular Lines Example: Determine whether the line x + 3y = – 15 is perpendicular to – 3x + y = – 1 . Find the slope of each line. x + 3y = – 15 – 3x + y = – 1 The slopes are negative reciprocals so the lines are perpendicular.

Perpendicular Lines Example: Find the equation of the line that is perpendicular to the line – 2x + 5y = 3 and contains the point (2, – 3). Write the equation in slope-intercept form. Find the slope of the line. – 2x + 5y = 3 5y = 2x + 3 Continued.

Perpendicular Lines Example continued: Use the point-slope form to find the equation. Use the negative reciprocal slope. Simplify. Subtract 3 from both sides.