mrs. rivas find the slope of the line passing through the given points
TRANSCRIPT
HomeworkMrs. RivasFind the slope of the line passing through the given points.
1.
𝒎=𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
¿𝟖−𝟎−𝟔−𝟐
¿𝟖−𝟖
¿−𝟏
HomeworkMrs. RivasFind the slope of the line passing through the given points.
2.
¿−𝟑−𝟏−𝟗−𝟗
¿−𝟒−𝟏𝟖
¿𝟐𝟗
𝒎=𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
HomeworkMrs. RivasFind the slope of the line passing through the given points.
3.
¿𝟖−(−𝟏)𝟐−(−𝟑)
¿𝟖+𝟏𝟐+𝟑
¿𝟗𝟓
𝒎=𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
HomeworkMrs. RivasFind the slope of the line passing through the given points.
4.
¿𝟕𝟔
HomeworkMrs. RivasFind the slope of the line passing through the given points.
5.
¿−𝟒𝟑
HomeworkMrs. RivasGraph each line.
6.
Starting point(0,-4)
𝒚=𝒎𝒙+𝒃
𝟏𝟏
HomeworkMrs. RivasGraph each line.
7.
Starting point(0,3)
𝒚=𝒎𝒙+𝒃
𝟐𝟏
HomeworkMrs. RivasGraph each line.
8.
Starting point(0,0)
𝒚=𝒎𝒙+𝒃
𝟏𝟒
HomeworkMrs. RivasGraph each line.
9.
Starting point(0,-1)
𝒚=𝒎𝒙+𝒃
−𝟑𝟒
HomeworkMrs. RivasUse the given information to write an equation of each line.
10. slope -intercept
𝒚=𝒎𝒙+𝒃
𝒚=𝟏𝟑𝒙+𝟔
HomeworkMrs. RivasUse the given information to write an equation of each line.
11. slope -intercept
𝒚=𝒎𝒙+𝒃
𝒚=−𝟏𝟎𝒙−𝟑
HomeworkMrs. RivasUse the given information to write an equation of each line.
12. slope 5, passes through
𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)
𝒚 − (−𝟑 )=−𝟓 (𝒙−𝟐)
𝒚+𝟑=−𝟓 (𝒙−𝟐)
𝒚+𝟑=−𝟓 𝒙+𝟏𝟎𝒚=−𝟓 𝒙+𝟕
HomeworkMrs. RivasUse the given information to write an equation of each line.
13. Slope , passes through
𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)
𝒚 −𝟐=𝟑𝟒
(𝒙−(−𝟖))
𝒚 −𝟐=𝟑𝟒𝒙+𝟔
𝒚=𝟑𝟒𝒙+𝟖
HomeworkMrs. RivasUse the given information to write an equation of each line.
14. passes through and
𝒎=𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
¿−𝟐−𝟔𝟒−𝟎
¿−𝟖𝟒
¿−𝟐
𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)
𝒚 −𝟔=−𝟐(𝒙−𝟎)
𝒚 −𝟔=−𝟐 𝒙+𝟎
𝒚=−𝟐 𝒙+𝟔
HomeworkMrs. RivasUse the given information to write an equation of each line.
15. passes through and
𝒎=𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
¿−𝟒−𝟖𝟓−(−𝟏)
¿−𝟏𝟐𝟔
¿−𝟐
𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)
𝒚 −𝟖=−𝟐(𝒙−(−𝟏))
𝒚 −𝟖=−𝟐(𝒙+𝟏)
𝒚 −𝟖=−𝟐 𝒙−𝟐𝒚=−𝟐 𝒙+𝟔
HomeworkMrs. RivasWrite the equations of the horizontal and vertical lines through the given
point.16.
𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝑳𝒊𝒏𝒆 :𝒚=𝟔
𝑽𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝑳𝒊𝒏𝒆 :𝒙=𝟓
HomeworkMrs. RivasWrite the equations of the horizontal and vertical lines through the given
point.17.
𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝑳𝒊𝒏𝒆 :𝒚=−𝟑
𝑽𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝑳𝒊𝒏𝒆 :𝒙=−𝟐
HomeworkMrs. RivasWrite the equations of the horizontal and vertical lines through the given
point.18.
𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝑳𝒊𝒏𝒆 :𝒚=−𝟏
𝑽𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝑳𝒊𝒏𝒆 :𝒙=𝟖
HomeworkMrs. RivasWrite the equations of the horizontal and vertical lines through the given
point.19.
𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝑳𝒊𝒏𝒆 :𝒚=𝟎
𝑽𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝑳𝒊𝒏𝒆 :𝒙=𝟏𝟎
HomeworkMrs. RivasWrite each equation in slope-intercept form.
20.
𝒚 −𝟓=𝟑(𝒙 −𝟒)
𝒚 −𝟓=𝟑 𝒙−𝟏𝟐𝒚=𝟑 𝒙−𝟕
𝒚=𝒎𝒙+𝒃
HomeworkMrs. RivasWrite each equation in slope-intercept form.
21.
𝒚+𝟐=−𝟓 (𝒙−𝟏)
𝒚+𝟐=−𝟓 𝒙+𝟓𝒚=−𝟓 𝒙+𝟑
𝒚=𝒎𝒙+𝒃
HomeworkMrs. RivasWrite each equation in slope-intercept form.
22.
𝟐 𝒙+𝟒 𝒚=𝟖
𝒚=𝒎𝒙+𝒃
−𝟐 𝒙 −𝟐 𝒙𝟒 𝒚=−𝟐 𝒙+𝟖𝟒 𝟒 𝟒
𝒚=−𝟏𝟐𝒙+𝟐
HomeworkMrs. RivasWrite each equation in slope-intercept form.
23.
𝟏𝟎𝒚+𝟏𝟔𝒙+𝟒=𝟐 𝒚
𝒚=𝒎𝒙+𝒃
−𝟏𝟎𝒚 −𝟏𝟎𝒚𝟏𝟔𝒙+𝟒=−𝟖 𝒚−𝟖 −𝟖 −𝟖
𝒚=−𝟐 𝒙−𝟏𝟐
HomeworkMrs. Rivas24.Coordinate Geometry The vertices of a quadrilateral are , ,
, and .a. Write an equation for the line through A and B.
¿𝟒−𝟏
𝟐−(−𝟏)
¿𝟒−𝟏𝟐+𝟏
¿33=𝟏
𝒎=𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)
𝒚 −𝟏=𝟏(𝒙 −(−𝟏))
𝒚 −𝟏=𝟏(𝒙+𝟏)
𝒚 −𝟏=𝒙+𝟏𝒚=𝒙+𝟐
HomeworkMrs. Rivas24.Coordinate Geometry The vertices of a quadrilateral are , ,
, and .
b. Write an equation for the line through C and D.
¿−𝟐−(−𝟒)𝟎−𝟐
¿𝟐−𝟐
¿−𝟏
𝒎=𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)
𝒚 − (−𝟒 )=−𝟏(𝒙 −𝟐)
𝒚+𝟒=−(𝒙 −𝟐)
𝒚+𝟒=− 𝒙+𝟐𝒚=−𝒙−𝟐
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?
𝒚=𝒙+𝟐 𝒚=−𝒙−𝟐
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.
HomeworkMrs. RivasFor Exercises 25 and 26, are lines and parallel? Explain.
25.
ℓ𝟏 =𝟐−𝟎
𝟑−(−𝟑)
¿𝟐𝟔
¿𝟏𝟑
𝒎=𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
ℓ𝟐 =−𝟏−(−𝟑)𝟓−(−𝟏)
¿𝟐𝟔
¿𝟏𝟑
Yes, the lines are parallel because the have the same slopes.
HomeworkMrs. RivasFor Exercises 25 and 26, are lines and parallel? Explain.
26.
ℓ𝟏 =−𝟑−𝟔−𝟏−(−𝟑)
¿−𝟗𝟐
¿−𝟗𝟐
𝒎=𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
ℓ𝟐 =𝟎−𝟖𝟔−𝟒
¿−𝟖𝟐
¿−𝟒
No, the lines are NOT parallel because the don’t have the same slopes.
HomeworkMrs. RivasWrite an equation of the line parallel to the given line that contains.
27. “Same Slope”
𝒎=−𝟓 𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)𝒚 −(−𝟐)=−𝟓(𝒙−𝟓)
𝒚+𝟐=−𝟓 (𝒙−𝟓)Use the distributive property
𝒚+𝟐=−𝟓 𝒙+𝟐𝟓Solve for y:
𝒚=−𝟓 𝒙+𝟐𝟑
HomeworkMrs. RivasWrite an equation of the line parallel to the given line that contains.
28. “Same Slope”
𝒎=𝟐 𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)
𝒚 −𝟏=𝟐(𝒙 −𝟖)Use the distributive property
𝒚 −𝟏=𝟐 𝒙−𝟏𝟔Solve for y:
𝒚=𝟐 𝒙−𝟏𝟓
HomeworkMrs. RivasWrite an equation of the line parallel to the given line that contains.
29. “Same Slope”
𝒎=𝟐𝟑
𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)
𝒚 −𝟔=𝟐𝟑
(𝒙−𝟎)Use the distributive property
𝒚 −𝟔=𝟐𝟑𝒙−𝟎Solve for y:
𝒚=𝟐𝟑𝒙+𝟔
HomeworkMrs. RivasRewrite each equation in slope-intercept form, if necessary. Then
determine whether the lines are parallel. Explain.
30.
𝒚=𝒎𝒙+𝒃
𝟐 𝒚+𝟔 𝒙=𝟏𝟖−𝟔 𝒙 −𝟔 𝒙𝟐 𝒚=−𝟔 𝒙+𝟏𝟖𝟐 𝟐 𝟐
𝒚=−𝟑 𝒙+𝟗
𝟒 𝒚+𝟏𝟐𝒙=𝟐𝟒−𝟏𝟐𝒙 −𝟏𝟐𝒙𝟒 𝒚=−𝟏𝟐𝒙+𝟏𝟖𝟒 𝟒 𝟒
𝒚=−𝟑 𝒙+𝟗
Yes, the lines are parallel because the have the same slopes.
HomeworkMrs. RivasRewrite each equation in slope-intercept form, if necessary. Then
determine whether the lines are parallel. Explain.
31.
𝒚=𝒎𝒙+𝒃
𝒚=𝒙+𝟖 𝒙−𝟐𝒚=𝟒−𝒙 −𝒙
−𝟐 𝒚=−𝒙+𝟒−𝟐 −𝟐 −𝟐
𝒚=−𝟏𝟐𝒙−𝟐
No, the lines are NOT parallel because the don’t have the same slopes.
HomeworkMrs. RivasRewrite each equation in slope-intercept form, if necessary. Then
determine whether the lines are parallel. Explain.
32.
𝟒 𝒚 −𝟑 𝒙=𝟐𝟎+𝟑 𝒙 +𝟑 𝒙𝟒 𝒚=𝟑 𝒙+𝟐𝟎𝟒 𝟒 𝟒
𝒚=𝟑𝟒𝒙+𝟓
𝟐 𝒚=𝟑𝟐𝒙+𝟒
𝟐𝟐
𝟐
Yes, the lines are parallel because the have the same slopes.
32÷21¿32×12¿34
𝒚=𝟑𝟒𝒙+𝟐
HomeworkMrs. RivasUse slopes to determine whether the opposite sides of
quadrilateral WXYZ are parallel.
33.
𝑾 𝑿
𝒀𝒁
𝒎=𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
𝑾𝑿=−𝟏−(−𝟏)−𝟑−(−𝟏)
¿−𝟏+𝟏−𝟑+𝟏
¿𝟎−𝟐
¿𝟎
𝒁𝒀=𝟑−𝟒
𝟐−(−𝟐)
¿𝟑−𝟒𝟐+𝟐
¿−𝟏𝟒
¿−𝟏𝟒
HomeworkMrs. RivasUse slopes to determine whether the opposite sides of
quadrilateral WXYZ are parallel.
33.
𝑾 𝑿
𝒀𝒁
𝒎=𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
𝑾 𝒁=−𝟏−𝟑−𝟏−𝟐
¿−𝟒−𝟑
¿𝟒𝟑
𝟎
𝑿𝒀=𝟒−(−𝟏)−𝟐−(−𝟑)
¿𝟒+𝟏−𝟐+𝟑
¿𝟓−𝟏
−𝟏𝟒
No, the lines are NOT parallel because the don’t have the same slopes.
¿−𝟓
HomeworkMrs. RivasUse slopes to determine whether the opposite sides of
quadrilateral WXYZ are parallel.
34.
𝑾 𝑿
𝒀𝒁𝒎=
𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
𝑾𝑿=𝟒−𝟏
𝟐−(−𝟏)
¿𝟒−𝟏𝟐+𝟏
¿𝟑𝟑
¿𝟏
𝒁𝒀=−𝟐−𝟏𝟏−𝟒
¿−𝟑−𝟑
¿𝟏
Yes, the lines are parallel because the have the same slopes.
HomeworkMrs. RivasFor Exercises 35 and 36, are lines and perpendiular? Explain.
35.
ℓ𝟏 =−𝟒−(−𝟏)𝟏−(−𝟐)
¿−𝟒+𝟏𝟏+𝟐
¿−𝟓𝟑
𝒎=𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
ℓ𝟐 =−𝟖−(−𝟑)−𝟐−𝟓
¿−𝟖+𝟑−𝟕
¿𝟓𝟕
No, the lines are NOT Perpendicular because the don’t have opposite reciprocal slopes.
HomeworkMrs. RivasFor Exercises 35 and 36, are lines and perpendiular? Explain.
36.
ℓ𝟏 =−𝟐−𝟔−𝟏−(−𝟓)
¿−𝟐−𝟔−𝟏+𝟓
¿−𝟖𝟒
𝒎=𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
ℓ𝟐 =𝟑−𝟎
𝟏−(−𝟓)
¿𝟑−𝟎𝟏+𝟓
¿𝟏𝟐
¿−𝟐
¿𝟑𝟔
Yes, the lines are Perpendicular because the have opposite reciprocal slopes.
HomeworkMrs. RivasWrite an equation of the line perpendicular to the given line that
contains D.37. “Opposite Reciprocal slope”𝒎=
𝟏𝟑 𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)
𝒚 −𝟐=𝟏𝟑
(𝒙−𝟔)Use the distributive property
𝒚 −𝟐=𝟏𝟑𝒙−𝟐Solve for y:
𝒚=𝟏𝟑𝒙
HomeworkMrs. RivasWrite an equation of the line perpendicular to the given line that
contains D.38. “Opposite Reciprocal slope”
𝒎=−𝟐𝟏
=−𝟐 𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)𝒚 −(−𝟑)=−𝟐(𝒙−𝟎)
Use the distributive property
𝒚+𝟑=−𝟐 (𝒙−𝟎)
𝒚+𝟑=−𝟐 𝒙−𝟎Solve for y:
𝒚=−𝟐 𝒙−𝟑
HomeworkMrs. RivasWrite an equation of the line perpendicular to the given line that
contains D.39. “Opposite Reciprocal slope”𝒎=
𝟑𝟐 𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)
𝒚 −𝟏=𝟑𝟐
(𝒙−(−𝟖))
𝒚 −𝟏=𝟑𝟐
(𝒙+𝟖)Use the distributive property
𝒚 −𝟏=𝟑𝟐𝒙+𝟏𝟐
𝒚=𝟑𝟐𝒙+𝟏𝟑
Solve for y:
HomeworkMrs. RivasWrite an equation of the line perpendicular to the given line that
contains D.40. “Opposite Reciprocal slope”𝒎=−
𝟏𝟓 𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)
𝒚 −𝟐=−𝟏𝟓
(𝒙−𝟐)Use the distributive property
𝒚 −𝟐=−𝟏𝟓𝒙+
𝟐𝟓Solve for y:
25+21¿2+105
¿125 𝒚=−
𝟏𝟓𝒙+
𝟏𝟐𝟓