mrs. rivas
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Mrs. Rivas. Find the slope of the line passing through the given points. 1. Mrs. Rivas. Find the slope of the line passing through the given points. 2. Mrs. Rivas. Find the slope of the line passing through the given points. 3. Mrs. Rivas. - PowerPoint PPT PresentationTRANSCRIPT
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HomeworkMrs. RivasFind the slope of the line passing through the given points.
1.
π=ππβππ
ππβππ
ΒΏπβπβπβπ
ΒΏπβπ
ΒΏβπ
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HomeworkMrs. RivasFind the slope of the line passing through the given points.
2.
ΒΏβπβπβπβπ
ΒΏβπβππ
ΒΏππ
π=ππβππ
ππβππ
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HomeworkMrs. RivasFind the slope of the line passing through the given points.
3.
ΒΏπβ(βπ)πβ(βπ)
ΒΏπ+ππ+π
ΒΏππ
π=ππβππ
ππβππ
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HomeworkMrs. RivasFind the slope of the line passing through the given points.
4.
ΒΏππ
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HomeworkMrs. RivasFind the slope of the line passing through the given points.
5.
ΒΏβππ
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HomeworkMrs. RivasGraph each line.
6.
Starting point
π=ππ+π
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HomeworkMrs. RivasGraph each line.
7.
Starting point
π=ππ+π
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HomeworkMrs. RivasGraph each line.
8.
Starting point
π=ππ+π
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HomeworkMrs. RivasGraph each line.
9.
Starting point
π=ππ+π
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HomeworkMrs. RivasUse the given information to write an equation of each line.
10. slope -intercept
π=ππ+π
π=πππ+π
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HomeworkMrs. RivasUse the given information to write an equation of each line.
11. slope -intercept
π=ππ+π
π=βπππβπ
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HomeworkMrs. RivasUse the given information to write an equation of each line.
12. slope 5, passes through
π βππ=π(πβππ)
π β (βπ )=βπ (πβπ)
π+π=βπ (πβπ)
π+π=βπ π+πππ=βπ π+π
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HomeworkMrs. RivasUse the given information to write an equation of each line.
13. Slope , passes through
π βππ=π(πβππ)
π βπ=ππ
(πβ(βπ))
π βπ=πππ+π
π=πππ+π
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HomeworkMrs. RivasUse the given information to write an equation of each line.
14. passes through and
π=ππβππ
ππβππ
ΒΏβπβππβπ
ΒΏβππ
ΒΏβπ
π βππ=π(πβππ)
π βπ=βπ(πβπ)
π βπ=βπ π+π
π=βπ π+π
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HomeworkMrs. RivasUse the given information to write an equation of each line.
15. passes through and
π=ππβππ
ππβππ
ΒΏβπβππβ(βπ)
ΒΏβπππ
ΒΏβπ
π βππ=π(πβππ)
π βπ=βπ(πβ(βπ))
π βπ=βπ(π+π)
π βπ=βπ πβππ=βπ π+π
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HomeworkMrs. RivasWrite the equations of the horizontal and vertical lines through the given
point.16.
π―πππππππππ π³πππ :π=π
π½πππππππ π³πππ :π=π
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HomeworkMrs. RivasWrite the equations of the horizontal and vertical lines through the given
point.17.
π―πππππππππ π³πππ :π=βπ
π½πππππππ π³πππ :π=βπ
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HomeworkMrs. RivasWrite the equations of the horizontal and vertical lines through the given
point.18.
π―πππππππππ π³πππ :π=βπ
π½πππππππ π³πππ :π=π
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HomeworkMrs. RivasWrite the equations of the horizontal and vertical lines through the given
point.19.
π―πππππππππ π³πππ :π=π
π½πππππππ π³πππ :π=ππ
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HomeworkMrs. RivasWrite each equation in slope-intercept form.
20.
π βππ=π(πβππ)
π βπ=π(π βπ)
π βπ=π πβπππ=π πβπ
π=ππ+π
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HomeworkMrs. RivasWrite each equation in slope-intercept form.
21.
π βππ=π(πβππ)
π+π=βπ (πβπ)
π+π=βπ π+ππ=βπ π+π
π=ππ+π
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HomeworkMrs. RivasWrite each equation in slope-intercept form.
22.
π π+π π=π
π=ππ+π
βπ π βπ ππ π=βπ π+ππ π π
π=βπππ+π
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HomeworkMrs. RivasWrite each equation in slope-intercept form.
23.
πππ+πππ+π=π π
π=ππ+π
βπππ βππππππ+π=βπ πβπ βπ βπ
π=βπ πβππ
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HomeworkMrs. Rivas24.Coordinate Geometry The vertices of a quadrilateral are , ,
, and .a. Write an equation for the line through A and B.
ΒΏπβπ
πβ(βπ)
ΒΏπβππ+π
ΒΏ33=π
π=ππβππ
ππβππ
π βππ=π(πβππ)
π βπ=π(π β(βπ))
π βπ=π(π+π)
π βπ=π+ππ=π+π
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HomeworkMrs. Rivas24.Coordinate Geometry The vertices of a quadrilateral are , ,
, and .
b. Write an equation for the line through C and D.
ΒΏβπβ(βπ)πβπ
ΒΏπβπ
ΒΏβπ
π=ππβππ
ππβππ
π βππ=π(πβππ)
π β (βπ )=βπ(π βπ)
π+π=β(π βπ)
π+π=β π+ππ=βπβπ
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HomeworkMrs. Rivas24.Coordinate Geometry The vertices of a quadrilateral are , ,
, and .c. Without graphing the lines, what can you tell about the lines from their
slopes?
π=π+π π=βπβπ
One line has a positive slope and the other has a negative slope.
We can also say that they are perpendicular since their slopes are opposite reciprocal.
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HomeworkMrs. RivasFor Exercises 25 and 26, are lines and parallel? Explain.
25.
βπ =πβπ
πβ(βπ)
ΒΏππ
ΒΏππ
π=ππβππ
ππβππ
βπ =βπβ(βπ)πβ(βπ)
ΒΏππ
ΒΏππ
Yes, the lines are parallel because the have the same slopes.
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HomeworkMrs. RivasFor Exercises 25 and 26, are lines and parallel? Explain.
26.
βπ =βπβπβπβ(βπ)
ΒΏβππ
ΒΏβππ
π=ππβππ
ππβππ
βπ =πβππβπ
ΒΏβππ
ΒΏβπ
No, the lines are NOT parallel because the donβt have the same slopes.
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HomeworkMrs. RivasWrite an equation of the line parallel to the given line that contains.
27. βSame Slopeβ
π=βπ π βππ=π(πβππ)π β(βπ)=βπ(πβπ)
π+π=βπ (πβπ)Use the distributive property
π+π=βπ π+ππSolve for y:
π=βπ π+ππ
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HomeworkMrs. RivasWrite an equation of the line parallel to the given line that contains.
28. βSame Slopeβ
π=π π βππ=π(πβππ)
π βπ=π(π βπ)Use the distributive property
π βπ=π πβππSolve for y:
π=π πβππ
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HomeworkMrs. RivasWrite an equation of the line parallel to the given line that contains.
29. βSame Slopeβ
π=ππ
π βππ=π(πβππ)
π βπ=ππ
(πβπ)Use the distributive property
π βπ=πππβπSolve for y:
π=πππ+π
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HomeworkMrs. RivasRewrite each equation in slope-intercept form, if necessary. Then
determine whether the lines are parallel. Explain.
30.
π=ππ+π
π π+π π=ππβπ π βπ ππ π=βπ π+πππ π π
π=βπ π+π
π π+πππ=ππβπππ βππππ π=βπππ+πππ π π
π=βπ π+π
Yes, the lines are parallel because the have the same slopes.
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HomeworkMrs. RivasRewrite each equation in slope-intercept form, if necessary. Then
determine whether the lines are parallel. Explain.
31.
π=ππ+π
π=π+π πβππ=πβπ βπ
βπ π=βπ+πβπ βπ βπ
π=βπππβπ
No, the lines are NOT parallel because the donβt have the same slopes.
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HomeworkMrs. RivasRewrite each equation in slope-intercept form, if necessary. Then
determine whether the lines are parallel. Explain.
32.
π π βπ π=ππ+π π +π ππ π=π π+πππ π π
π=πππ+π
π π=πππ+π
ππ
π
Yes, the lines are parallel because the have the same slopes.
32Γ·21ΒΏ32Γ12ΒΏ34
π=πππ+π
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HomeworkMrs. RivasUse slopes to determine whether the opposite sides of
quadrilateral WXYZ are parallel.
33.
πΎ πΏ
πππ=
ππβππ
ππβππ
πΎπΏ=βπβ(βπ)βπβ(βπ)
ΒΏβπ+πβπ+π
ΒΏπβπ
ΒΏπ
ππ=πβπ
πβ(βπ)
ΒΏπβππ+π
ΒΏβππ
ΒΏβππ
No, the lines are NOT parallel because the donβt have the same slopes.
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HomeworkMrs. RivasUse slopes to determine whether the opposite sides of
quadrilateral WXYZ are parallel.
34.
πΎ πΏ
πππ=
ππβππ
ππβππ
πΎπΏ=πβπ
πβ(βπ)
ΒΏπβππ+π
ΒΏππ
ΒΏπ
ππ=βπβππβπ
ΒΏβπβπ
ΒΏπ
Yes, the lines are parallel because the have the same slopes.
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HomeworkMrs. RivasFor Exercises 35 and 36, are lines and perpendiular? Explain.
35.
βπ =βπβ(βπ)πβ(βπ)
ΒΏβπ+ππ+π
ΒΏβππ
π=ππβππ
ππβππ
βπ =βπβ(βπ)βπβπ
ΒΏβπ+πβπ
ΒΏππ
No, the lines are NOT Perpendicular because the donβt have opposite reciprocal slopes.
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HomeworkMrs. RivasFor Exercises 35 and 36, are lines and perpendiular? Explain.
36.
βπ =βπβπβπβ(βπ)
ΒΏβπβπβπ+π
ΒΏβππ
π=ππβππ
ππβππ
βπ =πβπ
πβ(βπ)
ΒΏπβππ+π
ΒΏππ
ΒΏβπ
ΒΏππ
Yes, the lines are Perpendicular because the have opposite reciprocal slopes.
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HomeworkMrs. RivasWrite an equation of the line perpendicular to the given line that
contains D.37. βOpposite Reciprocal slopeβπ=
ππ π βππ=π(πβππ)
π βπ=ππ
(πβπ)Use the distributive property
π βπ=πππβπSolve for y:
π=πππ
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HomeworkMrs. RivasWrite an equation of the line perpendicular to the given line that
contains D.38. βOpposite Reciprocal slopeβ
π=βππ
=βπ π βππ=π(πβππ)π β(βπ)=βπ(πβπ)
Use the distributive property
π+π=βπ (πβπ)
π+π=βπ πβπSolve for y:
π=βπ πβπ
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HomeworkMrs. RivasWrite an equation of the line perpendicular to the given line that
contains D.39. βOpposite Reciprocal slopeβπ=
ππ π βππ=π(πβππ)
π βπ=ππ
(πβ(βπ))
π βπ=ππ
(π+π)Use the distributive property
π βπ=πππ+ππ
π=πππ+ππ
Solve for y:
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HomeworkMrs. RivasWrite an equation of the line perpendicular to the given line that
contains D.40. βOpposite Reciprocal slopeβπ=β
ππ π βππ=π(πβππ)
π βπ=βππ
(πβπ)Use the distributive property
π βπ=βπππ+
ππSolve for y:
25+21ΒΏ2+105
ΒΏ125 π=β
πππ+
πππ