AIM: Find parallel and perpendicular slopes Geometry Week 7 10-17-16 & 10-18-16 Grab your TEAM folders. Put your ID on and cell phone away. Find your green formula sheet. AIM: Find parallel and perpendicular slopes

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

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

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

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

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

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

Example 2: Slope intercept form Find the slope from the equation: 1) y = -5x + 3 2) y= 3 4 𝑥 −1 m = -5 m = 3 4 3) y = -11 4) x = 2 HOY m = 0 VUX m = undefined

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

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 = − 7 5 m = 4 //m = − 7 5 //m = 4 c) x = -5 d) y = - 6 m = undefined m = 0 //m = undefined //m = 0

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

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 = − 7 5 m = 4 1 ⊥m = 5 7 ⊥m = − 1 4 c) x = -5 d) y = - 6 m = undefined m = 0 ⊥m = 0 ⊥m = undefined

HW Complete the parallel lines worksheet.