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