Precalculus with limits Larson

1. 1.1 Parallel and
Perpendicular Lines
Precalculus

2. 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.

3. 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

4. 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

5. Now try independently
 Checkpoint
 Exercise 67 (a) pg 12
 Extra Examples73, 68, 74, 76
MAP TAP 2003-2004 Parallel and Perpendicular Lines 5

6. 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.

7. 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
m2
m1

8. 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

9. Now Try
 Check point
 Exercise 67 (b) pg 12
 Extra Examples73, 68, 74, 76
MAP TAP 2003-2004 Parallel and Perpendicular Lines 9

10. 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

11. MAP TAP 2003-2004 Parallel and Perpendicular Lines 11
End Show

12. 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

13. 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

14. 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 (__,__)

15. 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 (__,__)

16. 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
m2
m1

17. 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 (__,-__)

18. 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 (__, __)

19. 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 (__,__)