Parallel and perpendicular_lines 1.1
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1.1 Parallel and Perpendicular Lines Precalculus
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Transcript of Parallel and perpendicular_lines 1.1
1.1 Parallel and Perpendicular LinesPrecalculus
MAP TAP 2003-2004 Parallel and Perpendicular Lines 2
Teacher Page Content: Write the equation of a parallel or
perpendicular line to a given line, in slope intercept form.
Parallel and Perpendicular Lines 3
Parallel Lines Two distinct non-vertical lines are
parallel if and only if their slopes are equal. If l1║l2, then m1= m2.
If m1= m2, then l1║l2.
l1 l2
m1 m2
MAP TAP 2003-2004 Parallel and Perpendicular Lines 4
Write the equation of the line that passes through (2,-1) and is parallel to 2x – 3y = 5.
m = 2/3 and the point is (2,-1)
y = mx+b
-1 = 2/3(2)+b
-1 = 4/3+b
-7/3 = b
y = 2/3x-7/3
Now try independently Checkpoint Exercise 67 (a) pg 12
Extra Examples73, 68, 74, 76
MAP TAP 2003-2004 Parallel and Perpendicular Lines 5
MAP TAP 2003-2004 Parallel and Perpendicular Lines 6
Write the equation of the line that passes through (2,1) and is parallel to 4x – 2y = 3.
MAP TAP 2003-2004 Parallel and Perpendicular Lines 7
Perpendicular Lines Two non-vertical lines are
perpendicular if and only if their slopes are negative reciprocals of each other, and the product of their slopes is -1. If l1┴l2, then m1 ● m2= -1.
If m1= -1/m2 , then l1┴l2.
l1
l2
m2m1
MAP TAP 2003-2004 Parallel and Perpendicular Lines 8
Write the equation of the line that passes through (2,-1) and is perpendicular to 2x- 3y =5.
m = 2/3 and the point is (2,-1)
y = mx+b
y = 2/3x – 5/3
-1 = -3/2(2)+b
-1 = -3+b
2 = b
y = -3/2x+2
Now Try Check point Exercise 67 (b) pg 12
Extra Examples73, 68, 74, 76
MAP TAP 2003-2004 Parallel and Perpendicular Lines 9
Write the equation of the line that passes through (2,1) and is perpendicular to y = 4x – 2y =3.
MAP TAP 2003-2004 Parallel and Perpendicular Lines 10
MAP TAP 2003-2004 Parallel and Perpendicular Lines 11
End Show
MAP TAP 2003-2004 Parallel and Perpendicular Lines 12
Parallel Lines Two non-vertical lines are parallel if
and only if their slopes are equal. If l1║l2, then m1= m2.
If m1= m2, then l1║l2.
l1 l2
m1 m2
MAP TAP 2003-2004 Parallel and Perpendicular Lines 13
Write the equation of the line that passes through (3,6) and is parallel to y = 2/3x+2.
m = _____ and the point is (__,__)
y = mx+b
MAP TAP 2003-2004 Parallel and Perpendicular Lines 14
Write the equation of the line that passes through (4,-5) and is parallel to y = -2x-4.
m = ____ and the point is (__,__)
MAP TAP 2003-2004 Parallel and Perpendicular Lines 15
Write the equation of the line that passes through (-6,4) and is parallel to y=1/3x-1.
m=___ and the point is (__,__)
MAP TAP 2003-2004 Parallel and Perpendicular Lines 16
Perpendicular Lines Two non-vertical lines are
perpendicular if and only if the product of their slopes is -1. If l1┴l2, then m1 ● m2= -1.
If m1● m2 = -1, then l1┴l2.l1
l2
m2m1
MAP TAP 2003-2004 Parallel and Perpendicular Lines 17
Write the equation of the line that passes through (6,-5) and is perpendicular to y = 2x+3.
m = ___ and the point is (__,-__)
MAP TAP 2003-2004 Parallel and Perpendicular Lines 18
Write the equation of the line that passes through (6,-7) and is perpendicular to y = 2/3x+1.
m = ____ and the point is (__, __)
MAP TAP 2003-2004 Parallel and Perpendicular Lines 19
Write the equation of the line that passes through (-4,-3) and is perpendicular to y = x+6.
m = ___ and the point is (__,__)
