1. Warm Up x – 5 = 0 Write the Standard Form equation of
the line that passes through the points (5, 2) and (5, –3).
m = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1
= −3 −2 5 −5
x = 5
= −5 0
x – 5 = 0
undefined

2. Parallel & Perpendicular Lines
Parallel Lines
- coplanar lines that do not intersect
- have the same slope and different
y-intercepts
Perpendicular Lines
- intersect to form 4 right angles
- slopes are the opposite sign and reciprocal of one another

3. 1. y = 3x – 2 2. y = 8x – 1 x + 3y = –9 7x – y – 1 = 0 3y = –x – 9
Find the slope of each line. Then determine whether the lines are parallel, perpendicular, or neither…
1. y = 3x – y = 8x – 1
x + 3y = – x – y – 1 = 0
3y = –x – 9
–y = –7x + 1
y = – 1 3 x – 3
y = 7x – 1
m = – 1 3
m = 3
m = 8
m = 7
Perpendicular Lines
Neither

4. 3. y = x – 9 4. y = 2x + 4 x – y + 9 = 0 x + 2y + 10 = 0 2y = –x – 10
Find the slope of each line. Then determine whether the lines are parallel, perpendicular, or neither…
3. y = x – y = 2x + 4
x – y + 9 = x + 2y + 10 = 0
2y = –x – 10
–y = –x – 9
y = x + 9
y = − 1 2 x – 5
m = – 1 2
m = 1
m = 1
m = 2
Parallel Lines
Perpendicular Lines

5. 4x – y + 3 = 0 –y = –4x – 3 m = 4, (2, –3) y – 𝑦 1 = m(x – 𝑥 1 )
5. Write the standard form equation of the line that passes through (2, –3) and is parallel to the line…
4x – y + 3 = 0
–y = –4x – 3
m = 4, (2, –3)
y – 𝑦 1 = m(x – 𝑥 1 )
y = 4x + 3
y – (–3) = 4(x – 2)
m = 4
y + 3 = 4(x – 2)
4x – y – 11 = 0
y + 3 = 4x – 8

6. 3x + 2y + 1 = 0 m = – 3 2 , (3, –5) –3y = –2x – 6 y = 2 3 x + 2
6. Write the standard form equation of the line that passes through (3, –5) and is perpendicular to the line…
2x – 3y + 6 = 0
–3y = –2x – 6
m = – 3 2 , (3, –5)
y = 2 3 x + 2
y – 𝑦 1 = m(x – 𝑥 1 )
y – (–5) = – (x – 3)
m = 2 3
y + 5 = – (x – 3)
2y + 10 = –3x + 9
y + 5 = – 3 2 x
3x + 2y + 1 = 0

7. 7. a. Write the standard form equation of the line that passes through (2, 3) and is parallel to the line…
y – 5 = 0
b. What is the equation of the line that is perpendicular ?
y = 3
m = 0
m = 0
y – 3 = 0
x = 2
m = 0
m = undefined
x – 2 = 0

8. 8. a. Write the standard form equation of the line that passes through (–1, 4) and is parallel to the line…
x + 3 = 0
b. What is the equation of the line that is perpendicular ?
x = –1
m = undefined
x + 1 = 0
m = undefined
y = 4
m = undefined
y – 4 = 0
m = 0

9. 9. For what value of k is the graph of
kx – 7y + 10 = 0 parallel to the graph of 8x – 14y + 3 = 0? For what value of k are the graphs perpendicular?
parallel
kx – 7y + 10 = 0
8x – 14y + 3 = 0
𝑘 7 = 4 7
–7y = –kx – 10
–14y = –8x – 3
y = 𝑘 7 x
k = 4
y = x
perpendicular
m = 𝑘 7
y = 4 7 x
4k = –49
𝑘 7 = – 7 4
k = − 49 4
m = 4 7

10. 10. For what value of k is the graph of
2x – ky + 5 = 0 parallel to the graph of
3x + 7y + 15 = 0? For what value of k are the graphs perpendicular?
parallel
2x – ky + 5 = 0
3x + 7y + 15 = 0
2 𝑘 = – 3 7
–3k = 14
–ky = –2x – 5
7y = –3x – 15
y = 2 𝑘 x + 5 𝑘
k = – 14 3
y = – 3 7 x – 15 7
m = 2 𝑘
perpendicular
m = – 3 7
7k = 6
2 𝑘 = 7 3
k = 6 7