1. Mrs. Rivas 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = 𝟖−𝟎 −𝟔−𝟐 = 𝟖 −𝟖 =−𝟏
Find the slope of the line passing through the given points.
1. (2, 0), (6, 8)
𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
= 𝟖−𝟎 −𝟔−𝟐
= 𝟖 −𝟖
=−𝟏

2. Mrs. Rivas 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = −𝟑−𝟏 −𝟗−𝟗 = −𝟒 −𝟏𝟖 = 𝟐 𝟗
Find the slope of the line passing through the given points.
2. (9, 1), (9, 3)
𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
= −𝟑−𝟏 −𝟗−𝟗
= −𝟒 −𝟏𝟖
= 𝟐 𝟗

3. Mrs. Rivas 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = 𝟖−(−𝟏) 𝟐−(−𝟑) = 𝟖+𝟏 𝟐+𝟑 = 𝟗 𝟓
Find the slope of the line passing through the given points.
3. (3, 1), (2, 8)
𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
= 𝟖−(−𝟏) 𝟐−(−𝟑)
= 𝟖+𝟏 𝟐+𝟑
= 𝟗 𝟓

4. Mrs. Rivas
Find the slope of the line passing through the given points. 4.
= 𝟕 𝟔

5. Mrs. Rivas
Find the slope of the line passing through the given points. 5.
=− 𝟒 𝟑

6. Mrs. Rivas 6. 𝑦 = 𝑥 − 4 𝟏 𝟏 𝒚=𝒎𝒙+𝒃 Graph each line. Starting point
(0,-4)
𝟏 𝟏

7. Mrs. Rivas 7. 𝑦 = 2𝑥 + 3 𝟐 𝟏 𝒚=𝒎𝒙+𝒃 Graph each line. Starting point
(0,3)

8. Mrs. Rivas 8. 𝑦 = 1 4 𝑥 𝟏 𝟒 𝒚=𝒎𝒙+𝒃 Graph each line. Starting point
8. 𝑦 = 1 4 𝑥
Starting point
(0,0)
𝟏 𝟒

9. Mrs. Rivas 9. 𝑦 =− 3 4 𝑥−1 − 𝟑 𝟒 𝒚=𝒎𝒙+𝒃 Graph each line.
Starting point
(0,-1)
− 𝟑 𝟒

10. Mrs. Rivas
Use the given information to write an equation of each line.
10. slope 𝟏 𝟑 𝑦-intercept 𝟔
𝒚=𝒎𝒙+𝒃
𝒚= 𝟏 𝟑 𝒙+𝟔

11. Mrs. Rivas
Use the given information to write an equation of each line.
11. slope −𝟏𝟎 𝑦-intercept −𝟑
𝒚=𝒎𝒙+𝒃
𝒚=−𝟏𝟎𝒙−𝟑

12. Mrs. Rivas 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝒚− −𝟑 =−𝟓(𝒙−𝟐) 𝒚+𝟑=−𝟓(𝒙−𝟐) 𝒚+𝟑=−𝟓𝒙+𝟏𝟎
Use the given information to write an equation of each line.
12. slope 5, passes through (2, 3)
𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 )
𝒚− −𝟑 =−𝟓(𝒙−𝟐)
𝒚+𝟑=−𝟓(𝒙−𝟐)
𝒚+𝟑=−𝟓𝒙+𝟏𝟎
𝒚=−𝟓𝒙+𝟕

13. Mrs. Rivas 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝒚−𝟐= 𝟑 𝟒 (𝒙−(−𝟖)) 𝒚−𝟐= 𝟑 𝟒 𝒙+𝟔
Use the given information to write an equation of each line.
13. Slope 𝟑 𝟒 , passes through (8, 2)
𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 )
𝒚−𝟐= 𝟑 𝟒 (𝒙−(−𝟖))
𝒚−𝟐= 𝟑 𝟒 𝒙+𝟔
𝒚= 𝟑 𝟒 𝒙+𝟖

14. Mrs. Rivas 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝒚−𝟔=−𝟐(𝒙−𝟎)
Use the given information to write an equation of each line.
14. passes through (0, 6) and (4, 2)
𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 )
𝒚−𝟔=−𝟐(𝒙−𝟎)
= −𝟐−𝟔 𝟒−𝟎
𝒚−𝟔=−𝟐𝒙+𝟎
𝒚=−𝟐𝒙+𝟔
= −𝟖 𝟒
=−𝟐

15. Mrs. Rivas 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝒚−𝟖=−𝟐(𝒙−(−𝟏))
Use the given information to write an equation of each line.
15. passes through (1, 8) and (5, 4)
𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 )
𝒚−𝟖=−𝟐(𝒙−(−𝟏))
= −𝟒−𝟖 𝟓−(−𝟏)
𝒚−𝟖=−𝟐(𝒙+𝟏)
𝒚−𝟖=−𝟐𝒙−𝟐
= −𝟏𝟐 𝟔
𝒚=−𝟐𝒙+𝟔
=−𝟐

16. Mrs. Rivas 𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝑳𝒊𝒏𝒆:𝒚=𝟔 𝑽𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝑳𝒊𝒏𝒆:𝒙=𝟓 16. (5, 6)
Write the equations of the horizontal and vertical lines through the given point.
16. (5, 6)
𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝑳𝒊𝒏𝒆:𝒚=𝟔
𝑽𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝑳𝒊𝒏𝒆:𝒙=𝟓

17. Mrs. Rivas 𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝑳𝒊𝒏𝒆:𝒚=−𝟑 𝑽𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝑳𝒊𝒏𝒆:𝒙=−𝟐 17. (2, 3)
Write the equations of the horizontal and vertical lines through the given point.
17. (2, 3)
𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝑳𝒊𝒏𝒆:𝒚=−𝟑
𝑽𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝑳𝒊𝒏𝒆:𝒙=−𝟐

18. Mrs. Rivas 𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝑳𝒊𝒏𝒆:𝒚=−𝟏 𝑽𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝑳𝒊𝒏𝒆:𝒙=𝟖 18. (8, 1)
Write the equations of the horizontal and vertical lines through the given point.
18. (8, 1)
𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝑳𝒊𝒏𝒆:𝒚=−𝟏
𝑽𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝑳𝒊𝒏𝒆:𝒙=𝟖

19. Mrs. Rivas 𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝑳𝒊𝒏𝒆:𝒚=𝟎 𝑽𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝑳𝒊𝒏𝒆:𝒙=𝟏𝟎 19. (10, 0)
Write the equations of the horizontal and vertical lines through the given point.
19. (10, 0)
𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝑳𝒊𝒏𝒆:𝒚=𝟎
𝑽𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝑳𝒊𝒏𝒆:𝒙=𝟏𝟎

20. Mrs. Rivas 𝒚−𝟓=𝟑(𝒙−𝟒) 𝒚−𝟓=𝟑𝒙−𝟏𝟐 𝒚=𝟑𝒙−𝟕 𝒚=𝒎𝒙+𝒃 20. 𝑦 − 5 = 3(𝑥 − 4)
Write each equation in slope-intercept form.
20. 𝑦 − 5 = 3(𝑥 − 4)
𝒚−𝟓=𝟑(𝒙−𝟒)
𝒚−𝟓=𝟑𝒙−𝟏𝟐
𝒚=𝟑𝒙−𝟕

21. Mrs. Rivas 𝒚+𝟐=−𝟓(𝒙−𝟏) 𝒚+𝟐=−𝟓𝒙+𝟓 𝒚=−𝟓𝒙+𝟑 𝒚=𝒎𝒙+𝒃 21. 𝑦 + 2 =−5(𝑥 − 1)
Write each equation in slope-intercept form.
21. 𝑦 + 2 =−5(𝑥 − 1)
𝒚+𝟐=−𝟓(𝒙−𝟏)
𝒚+𝟐=−𝟓𝒙+𝟓
𝒚=−𝟓𝒙+𝟑

22. Mrs. Rivas 𝟐𝒙+𝟒𝒚=𝟖 −𝟐𝒙 −𝟐𝒙 𝟒𝒚=−𝟐𝒙+𝟖 𝟒 𝟒 𝟒 𝒚=− 𝟏 𝟐 𝒙+𝟐 𝒚=𝒎𝒙+𝒃
Write each equation in slope-intercept form.
𝒚=𝒎𝒙+𝒃
22. 2𝑥 + 4𝑦 = 8
𝟐𝒙+𝟒𝒚=𝟖
−𝟐𝒙
−𝟐𝒙
𝟒𝒚=−𝟐𝒙+𝟖 𝟒 𝟒 𝟒
𝒚=− 𝟏 𝟐 𝒙+𝟐

23. Mrs. Rivas 𝟏𝟎𝒚+𝟏𝟔𝒙+𝟒=𝟐𝒚 −𝟏𝟎𝒚 −𝟏𝟎𝒚 𝟏𝟔𝒙+𝟒=−𝟖𝒚 −𝟖 −𝟖 −𝟖 𝒚=−𝟐𝒙− 𝟏 𝟐 𝒚=𝒎𝒙+𝒃
Write each equation in slope-intercept form.
23. 10𝑦 + 16𝑥 + 4 = 2𝑦
𝟏𝟎𝒚+𝟏𝟔𝒙+𝟒=𝟐𝒚
−𝟏𝟎𝒚
−𝟏𝟎𝒚
𝟏𝟔𝒙+𝟒=−𝟖𝒚 −𝟖 −𝟖 −𝟖
𝒚=−𝟐𝒙− 𝟏 𝟐

24. Mrs. Rivas 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 𝒚−𝟏=𝟏(𝒙−(−𝟏))
24.Coordinate Geometry The vertices of a quadrilateral are 𝐴(−1, 1), 𝐵(2, 4),
𝐶(2, −4), and 𝐷(0, −2).
a. Write an equation for the line through A and B.
𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 )
𝒚−𝟏=𝟏(𝒙−(−𝟏))
= 𝟒−𝟏 𝟐−(−𝟏)
𝒚−𝟏=𝟏(𝒙+𝟏)
𝒚−𝟏=𝒙+𝟏
= 𝟒−𝟏 𝟐+𝟏
𝒚=𝒙+𝟐
= 3 3 =𝟏

25. Mrs. Rivas 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 𝒚− −𝟒 =−𝟏(𝒙−𝟐)
24.Coordinate Geometry The vertices of a quadrilateral are 𝐴(−1, 1), 𝐵(2, 4),
𝐶(2, −4), and 𝐷(0, −2).
b. Write an equation for the line through C and D.
𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 )
𝒚− −𝟒 =−𝟏(𝒙−𝟐)
= −𝟐−(−𝟒) 𝟎−𝟐
𝒚+𝟒=−(𝒙−𝟐)
𝒚+𝟒=−𝒙+𝟐
= 𝟐 −𝟐
𝒚=−𝒙−𝟐
=−𝟏

26. Mrs. Rivas
24.Coordinate Geometry The vertices of a quadrilateral are 𝐴(−1, 1), 𝐵(2, 4),
𝐶(2, −4), and 𝐷(0, −2).
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.

27. Mrs. Rivas
For Exercises 25 and 26, are lines ℓ 𝟏 and ℓ 𝟐 parallel? Explain.
25.
𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
ℓ 𝟏 = 𝟐−𝟎 𝟑−(−𝟑)
ℓ 𝟐 = −𝟏−(−𝟑) 𝟓−(−𝟏)
= 𝟐 𝟔
= 𝟐 𝟔
= 𝟏 𝟑
= 𝟏 𝟑
Yes, the lines are parallel because the have the same slopes.

28. Mrs. Rivas 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = −𝟗 𝟐 =−𝟒 =− 𝟗 𝟐
For Exercises 25 and 26, are lines ℓ 𝟏 and ℓ 𝟐 parallel? Explain.
26.
𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
ℓ 𝟏 = −𝟑−𝟔 −𝟏−(−𝟑)
ℓ 𝟐 = 𝟎−𝟖 𝟔−𝟒
= −𝟗 𝟐
= −𝟖 𝟐
=−𝟒
=− 𝟗 𝟐
No, the lines are NOT parallel because the don’t have the same slopes.

29. Mrs. Rivas 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝒚−(−𝟐)=−𝟓(𝒙−𝟓) 𝒚+𝟐=−𝟓(𝒙−𝟓) 𝒚+𝟐=−𝟓𝒙+𝟐𝟓
Write an equation of the line parallel to the given line that contains 𝑪.
27. 𝐶 5,−2 ; 𝑦 =−5𝑥 + 3
“Same Slope”
𝒎 =−𝟓
𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 )
𝒚−(−𝟐)=−𝟓(𝒙−𝟓)
Use the distributive property
𝒚+𝟐=−𝟓(𝒙−𝟓)
𝒚+𝟐=−𝟓𝒙+𝟐𝟓
Solve for y:
𝒚=−𝟓𝒙+𝟐𝟑

30. Mrs. Rivas 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝒚−𝟏=𝟐(𝒙−𝟖) 𝒚−𝟏=𝟐𝒙−𝟏𝟔 𝒚=𝟐𝒙−𝟏𝟓
Write an equation of the line parallel to the given line that contains 𝑪.
28. 𝐶(8, 1); 𝑦 = 2𝑥 + 6
“Same Slope”
𝒎 =𝟐
𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 )
𝒚−𝟏=𝟐(𝒙−𝟖)
Use the distributive property
𝒚−𝟏=𝟐𝒙−𝟏𝟔
Solve for y:
𝒚=𝟐𝒙−𝟏𝟓

31. Mrs. Rivas 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝒚−𝟔= 𝟐 𝟑 (𝒙−𝟎) 𝒚−𝟔= 𝟐 𝟑 𝒙−𝟎 𝒚= 𝟐 𝟑 𝒙+𝟔
Write an equation of the line parallel to the given line that contains 𝑪.
29. 𝐶(0, 6); 𝑦 = 2 3 𝑥 +3
“Same Slope”
𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 )
𝒎 = 𝟐 𝟑
𝒚−𝟔= 𝟐 𝟑 (𝒙−𝟎)
Use the distributive property
𝒚−𝟔= 𝟐 𝟑 𝒙−𝟎
Solve for y:
𝒚= 𝟐 𝟑 𝒙+𝟔

32. Mrs. Rivas 𝟐𝒚+𝟔𝒙=𝟏𝟖 𝟒𝒚+𝟏𝟐𝒙=𝟐𝟒 −𝟔𝒙 −𝟔𝒙 −𝟏𝟐𝒙 −𝟏𝟐𝒙 𝟐𝒚=−𝟔𝒙+𝟏𝟖 𝟒𝒚=−𝟏𝟐𝒙+𝟐𝟒 𝟐
𝒚=𝒎𝒙+𝒃
Rewrite each equation in slope-intercept form, if necessary. Then determine whether the lines are parallel. Explain.
30. 2𝑦 + 6𝑥 = 18
4𝑦+12𝑥=24
𝟐𝒚+𝟔𝒙=𝟏𝟖
𝟒𝒚+𝟏𝟐𝒙=𝟐𝟒
−𝟔𝒙
−𝟔𝒙
−𝟏𝟐𝒙
−𝟏𝟐𝒙
𝟐𝒚=−𝟔𝒙+𝟏𝟖
𝟒𝒚=−𝟏𝟐𝒙+𝟐𝟒 𝟐 𝟐 𝟐 𝟒 𝟒 𝟒
𝒚=−𝟑𝒙+𝟗
𝒚=−𝟑𝒙+𝟔
Yes, the lines are parallel because the have the same slopes.

33. Mrs. Rivas 𝒙−𝟐𝒚=𝟒 𝒚=𝒙+𝟖 −𝒙 −𝒙 −𝟐𝒚=−𝒙+𝟒 −𝟐 −𝟐 −𝟐 𝒚=− 𝟏 𝟐 𝒙−𝟐
𝒚=𝒎𝒙+𝒃
Rewrite each equation in slope-intercept form, if necessary. Then determine whether the lines are parallel. Explain.
31. 𝑦=𝑥+8
𝑥−2𝑦=4
𝒙−𝟐𝒚=𝟒
𝒚=𝒙+𝟖 −𝒙 −𝒙
−𝟐𝒚=−𝒙+𝟒 −𝟐 −𝟐 −𝟐
𝒚=− 𝟏 𝟐 𝒙−𝟐
No, the lines are NOT parallel because the don’t have the same slopes.

34. Mrs. Rivas 𝟐𝒚= 𝟑 𝟐 𝒙+𝟒 𝟒𝒚−𝟑𝒙=𝟐𝟎 𝟐 𝟐 +𝟑𝒙 +𝟑𝒙 𝟐 𝟒𝒚=𝟑𝒙+𝟐𝟎 𝟒 𝟒 𝟒
Rewrite each equation in slope-intercept form, if necessary. Then determine whether the lines are parallel. Explain.
32. 4𝑦 −3𝑥 =20
2𝑦= 3 2 𝑥+4
𝟐𝒚= 𝟑 𝟐 𝒙+𝟒
3 2 ÷ 2 1
= 3 2 × 1 2
= 3 4
𝟒𝒚−𝟑𝒙=𝟐𝟎 𝟐 𝟐
+𝟑𝒙
+𝟑𝒙 𝟐
𝟒𝒚=𝟑𝒙+𝟐𝟎 𝟒 𝟒 𝟒
𝒚= 𝟑 𝟒 𝒙+𝟐
𝒚= 𝟑 𝟒 𝒙+𝟓
Yes, the lines are parallel because the have the same slopes.

35. Mrs. Rivas 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 𝒁𝒀= 𝟑−𝟒 𝟐−(−𝟐) 𝑾𝑿= −𝟏−(−𝟏) −𝟑−(−𝟏)
Use slopes to determine whether the opposite sides of quadrilateral WXYZ are parallel.
𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
33.𝑊(−1, −1), 𝑋(−3, −1), 𝑌(−2, 4), 𝑍(2, 3) 𝒁 𝒀
𝒁𝒀= 𝟑−𝟒 𝟐−(−𝟐)
𝑾𝑿= −𝟏−(−𝟏) −𝟑−(−𝟏)
= 𝟑−𝟒 𝟐+𝟐
= −𝟏+𝟏 −𝟑+𝟏 𝑾 𝑿
= −𝟏 𝟒
= 𝟎 −𝟐
=− 𝟏 𝟒 =𝟎

36. Mrs. Rivas
Use slopes to determine whether the opposite sides of quadrilateral WXYZ are parallel.
𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
33.𝑊(−1, −1), 𝑋(−3, −1), 𝑌(−2, 4), 𝑍(2, 3) 𝒁
− 𝟏 𝟒 𝒀
𝑿𝒀= 𝟒−(−𝟏) −𝟐−(−𝟑)
𝑾𝒁= −𝟏−𝟑 −𝟏−𝟐
= 𝟒+𝟏 −𝟐+𝟑
= −𝟒 −𝟑 𝟎 𝑾 𝑿
= 𝟓 −𝟏
= 𝟒 𝟑
=−𝟓
No, the lines are NOT parallel because the don’t have the same slopes.

37. Mrs. Rivas
Use slopes to determine whether the opposite sides of quadrilateral WXYZ are parallel.
𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
34.𝑊(−1, 1), 𝑋(2, 4), 𝑌(4, 1), 𝑍(1, −2) 𝒁 𝒀
𝒁𝒀= −𝟐−𝟏 𝟏−𝟒
𝑾𝑿= 𝟒−𝟏 𝟐−(−𝟏)
= −𝟑 −𝟑 𝑾 𝑿
= 𝟒−𝟏 𝟐+𝟏
= 𝟑 𝟑 =𝟏 =𝟏
Yes, the lines are parallel because the have the same slopes.

38. Mrs. Rivas 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = −𝟒+𝟏 𝟏+𝟐 = −𝟖+𝟑 −𝟕 =− 𝟓 𝟑 = 𝟓 𝟕
For Exercises 35 and 36, are lines ℓ 𝟏 and ℓ 𝟐 perpendiular? Explain.
35.
𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
ℓ 𝟐 = −𝟖−(−𝟑) −𝟐−𝟓
ℓ 𝟏 = −𝟒−(−𝟏) 𝟏−(−𝟐)
= −𝟒+𝟏 𝟏+𝟐
= −𝟖+𝟑 −𝟕
=− 𝟓 𝟑
= 𝟓 𝟕
No, the lines are NOT Perpendicular because the don’t have opposite reciprocal slopes.

39. Mrs. Rivas 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = −𝟐−𝟔 −𝟏+𝟓 = 𝟑−𝟎 𝟏+𝟓 =− 𝟖 𝟒 = 𝟑 𝟔
For Exercises 35 and 36, are lines ℓ 𝟏 and ℓ 𝟐 perpendiular? Explain.
36.
𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏
ℓ 𝟐 = 𝟑−𝟎 𝟏−(−𝟓)
ℓ 𝟏 = −𝟐−𝟔 −𝟏−(−𝟓)
= −𝟐−𝟔 −𝟏+𝟓
= 𝟑−𝟎 𝟏+𝟓
=− 𝟖 𝟒
= 𝟑 𝟔
=−𝟐
= 𝟏 𝟐
Yes, the lines are Perpendicular because the have opposite reciprocal slopes.

40. Mrs. Rivas 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝒚−𝟐= 𝟏 𝟑 (𝒙−𝟔) 𝒚−𝟐= 𝟏 𝟑 𝒙−𝟐 𝒚= 𝟏 𝟑 𝒙
Write an equation of the line perpendicular to the given line that contains D.
37. 𝐷 6, 2 ; 𝑦 =−3𝑥 + 5
“Opposite Reciprocal slope”
𝒎 = 𝟏 𝟑
𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 )
𝒚−𝟐= 𝟏 𝟑 (𝒙−𝟔)
Use the distributive property
𝒚−𝟐= 𝟏 𝟑 𝒙−𝟐
Solve for y:
𝒚= 𝟏 𝟑 𝒙

41. Mrs. Rivas 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝒚−(−𝟑)=−𝟐(𝒙−𝟎) 𝒚+𝟑=−𝟐(𝒙−𝟎) 𝒚+𝟑=−𝟐𝒙−𝟎
Write an equation of the line perpendicular to the given line that contains D.
38. 𝐷 0, −3 ; 𝑦 = 1 2 𝑥 −7
“Opposite Reciprocal slope”
𝒎 =− 𝟐 𝟏 =−𝟐
𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 )
𝒚−(−𝟑)=−𝟐(𝒙−𝟎)
𝒚+𝟑=−𝟐(𝒙−𝟎)
Use the distributive property
𝒚+𝟑=−𝟐𝒙−𝟎
Solve for y:
𝒚=−𝟐𝒙−𝟑

42. Mrs. Rivas 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝒚−𝟏= 𝟑 𝟐 (𝒙−(−𝟖)) 𝒚−𝟏= 𝟑 𝟐 (𝒙+𝟖)
Write an equation of the line perpendicular to the given line that contains D.
39. 𝐷 −8,1 ; 𝑦 =− 2 3 𝑥+4
“Opposite Reciprocal slope”
𝒎 = 𝟑 𝟐
𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 )
𝒚−𝟏= 𝟑 𝟐 (𝒙−(−𝟖))
𝒚−𝟏= 𝟑 𝟐 (𝒙+𝟖)
Use the distributive property
𝒚−𝟏= 𝟑 𝟐 𝒙+𝟏𝟐
Solve for y:
𝒚= 𝟑 𝟐 𝒙+𝟏𝟑

43. Mrs. Rivas 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 𝒚−𝟐=− 𝟏 𝟓 (𝒙−𝟐) 𝒚−𝟐=− 𝟏 𝟓 𝒙+ 𝟐 𝟓
Write an equation of the line perpendicular to the given line that contains D.
40. 𝐷(2, 2); 𝑦 = 5𝑥 + 3
“Opposite Reciprocal slope”
𝒎 =− 𝟏 𝟓
𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 )
𝒚−𝟐=− 𝟏 𝟓 (𝒙−𝟐)
Use the distributive property
𝒚−𝟐=− 𝟏 𝟓 𝒙+ 𝟐 𝟓
Solve for y: =
= 12 5
𝒚=− 𝟏 𝟓 𝒙+ 𝟏𝟐 𝟓