Parallel and Perpendicular Lines Parallel Lines Two nonvertical

Parallel and Perpendicular Lines

Parallel Lines. . . ● Two non-vertical lines are parallel if and only if their slopes are equal. o If l 1║l 2, then m 1= m 2. o If m 1= m 2, then l 1║l 2. m 1 m 2 l 1 l 2

Check-In Questions ● Write the equation of a line that is parallel to the line y = 2/3 x+8. o y = 2/3 x-10 o y = 2/3 x+1234 ● Is the line y = 8/4 x-5 parallel to the line y = 2 x+7? o Yes. The two lines have equal slopes so they are parallel.

Perpendicular Lines ● Two non-vertical lines are perpendicular or orthogonal if and only if the product of their slopes is -1. m 2 o If l 1┴l 2, then m 1 ● m 2= -1. o If m 1● m 2 = -1, then l 1┴l 2. Perpendicular lines form right angles! l 1 m 2 m 1 l 2 l 1 m 1 l 2

Perpendicular Lines Continued ● The slopes of perpendicular lines are considered opposite reciprocals. o Opposite refers to either positive or negative. o Reciprocal refers to taking the multiplicative inverse of the fraction. § For example if the slope is x, the reciprocal or inverse is 1/x.

Check-In Question ● Write the equation of a line that is perpendicular to the line y = 5/4 x+7. o y = -4/5 x-10 ● Is the line y = -3/4 x-2 perpendicular to the line y = 12/9 x? o Yes. The slopes are opposite reciprocals of each other. o 12/9 = 4/3 is the opposite multiplicative inverse of -3/4.

End of Lesson!

Slides for Students

Parallel Lines. . . ● Two non-vertical lines are ______ if and only if their ____ are _____. o If l 1║l 2, then m 1___m 2. o If m 1= m 2, then l 1___l 2. m 1 m 2 l 1 l 2

Check-In Questions Submit your answers to the questions below using this form. ● Write the equation of a line that is parallel to the line y = 2/3 x+8. ● Is the line y = 8/4 x-5 parallel to the line y = 2 x+7?

Perpendicular Lines ● Two non-vertical lines are _____ or ______if and only if the _____ of their ____ is -1. m 2 o If l 1┴l 2, then m 1___m 2= -1. o If m 1● m 2 = -1, then l 1___l 2. Perpendicular lines form right angles! l 1 m 2 m 1 l 2 l 1 m 1 l 2

Perpendicular Lines Continued ● The____of perpendicular lines are considered ___________. o Opposite refers to either ____ or negative. o ____ refers to taking the multiplicative _______ of the fraction. § For example if the slope is x, the reciprocal or inverse is 1/x.

Check-In Question Submit your answers to the questions below using this form. ● Write the equation of a line that is perpendicular to the line y = 5/4 x+7. ● Is the line y = -3/4 x-2 perpendicular to the line y = 12/9 x?

End of Lesson!