1. AIM: Find parallel and perpendicular slopes
Geometry Week &
Grab your TEAM folders.
Put your ID on and cell phone away.
Find your green formula sheet.
AIM: Find parallel and perpendicular slopes

2. Bell-ringer: 1) Describe the relationship between <1 & <3
2) Solve for x.
3) Find both angle measures.
Given: m<1 = 3x m<3 = 2x + 12
1) Vertical angles 2) 3x + 9 = 2x x = 3
3) m<1 = m<2 = 18º

3. Slopes of lines the measure of steepness of the line
the rate of change between any two points on a line.
the measure of steepness of the line
Is represented by the letter m
Slope = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 𝑜𝑟 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛

4. Slopes of lines in the coordinate plane
Negative slope falls from left to right (line j)
Positive slope
rises from left to right (line k)
Zero slope horizontal (line m)
Undefined slope
vertical (line n) k m j n

5. H O Y V U X H: horizontal lines O: 0 slope
Y: equation is y = # ex: y = 3
V: vertical lines
U: undefined slope
X: equation is x = # ex: x = 3

6. Example 1: Finding slopes of lines
A) (-7, 4) & (5, -2) B) (3, 8) & (0, 8)
𝑥 𝑦 𝑥 𝑦 𝑥 𝑦 𝑥 𝑦 2
𝑚= −2 −4 5 −(−7) = −6 12 = − 𝑚= 8 − 8 0 − 3 = 0 −3 =0
𝑚= −1 2 = 1 −2 =− HOY

7. Example 1: Finding slopes of lines
C) (-1, -7) & (-1, -2) D) (5, 2) & (-1, 0)
M = 5 0 =undefined m= 1 3 = −1 −3
VUX

8. Example 2: Slope intercept form
Find the slope from the equation:
1) y = -5x ) y= 3 4 𝑥 −1
m = m = 3 4
3) y = ) x = HOY m = VUX m = undefined

9. Slopes of parallel lines
Two non-vertical lines are parallel if and only if they have the same slope
Any two vertical lines are parallel

10. Example 3) Parallel slopes
1) What will be a slope that is parallel to the following line?
a) y = − 7 5 𝑥+2 b) y = 4x – 1
m = − m = //m = − //m = 4
c) x = d) y = - 6
m = undefined m = 0 //m = undefined //m = 0

11. Slopes of perpendicular lines
Two non-vertical lines are perpendicular if and only if the product of their slopes is -1
This means their slopes are opposite reciprocals
Horizontal lines are perpendicular to vertical lines

12. Example 4) Perpendicular slopes
1) What will be a slope that is perpendicular to the following line?
a) y = − 7 5 𝑥+2 b) y = 4x – 1
m = − m = 4 1
⊥m = ⊥m = − 1 4
c) x = d) y = - 6
m = undefined m = ⊥m = ⊥m = undefined

13. HW
Complete the parallel lines worksheet.