mrs. rivas find the slope of the line passing through the given points
TRANSCRIPT
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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(0,-4)
π=ππ+π
ππ
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HomeworkMrs. RivasGraph each line.
7.
Starting point(0,3)
π=ππ+π
ππ
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HomeworkMrs. RivasGraph each line.
8.
Starting point(0,0)
π=ππ+π
ππ
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HomeworkMrs. RivasGraph each line.
9.
Starting point(0,-1)
π=ππ+π
βππ
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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 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+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
ππ
π=ππβππ
ππβππ
πΎπΏ=βπβ(βπ)βπβ(βπ)
ΒΏβπ+πβπ+π
ΒΏπβπ
ΒΏπ
ππ=πβπ
πβ(βπ)
ΒΏπβππ+π
ΒΏβππ
ΒΏβππ
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HomeworkMrs. RivasUse slopes to determine whether the opposite sides of
quadrilateral WXYZ are parallel.
33.
πΎ πΏ
ππ
π=ππβππ
ππβππ
πΎ π=βπβπβπβπ
ΒΏβπβπ
ΒΏππ
π
πΏπ=πβ(βπ)βπβ(βπ)
ΒΏπ+πβπ+π
ΒΏπβπ
βππ
No, the lines are NOT parallel because the donβt have the same slopes.
ΒΏβπ
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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