Slope and Rate of Change

Coordinate Grid II I III IV 3 Label the Quadrants: Which quadrant is Point B in? A 3 What is the ordered pair for Point A? B (7,2) III IV

𝑦=𝑚𝑥+𝑏 Slope-Intercept Form y-intercept Slope 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 Point on the line (x,y) Slope 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛

𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 Slope Formula Point 1: ( 𝑥 1 , 𝑦 1 ) When given two points, you can find the slope with the slop formula 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 Point 1: ( 𝑥 1 , 𝑦 1 ) Point 2: ( 𝑥 2 , 𝑦 2 )

Find the Slope! A. 3,4 𝑎𝑛𝑑 (5,12) B. −1,6 𝑎𝑛𝑑 (3,2) C. 2,−7 𝑎𝑛𝑑 (−1,3) 𝑚= 12−4 5−3 = 8 2 =4 A. 3,4 𝑎𝑛𝑑 (5,12) 𝑚= 2−6 3−(−1) = −4 4 =−1 B. −1,6 𝑎𝑛𝑑 (3,2) 𝑚= 3−(−7) −1−2 = 10 −3 C. 2,−7 𝑎𝑛𝑑 (−1,3) 𝑚= −1−(−1) −1−4 = 0 −5 =0 D. 4,−1 𝑎𝑛𝑑 (−3,−1) 𝑚= 8−11 5−5 = −3 0 =𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑 E. 5,11 𝑎𝑛𝑑 (5,8)

Identify the Slope and y-Intercept Slope: 4 y-int: −3 B. 𝑦=−𝑥 Slope: −1 y-int: 0 C. 3𝑦=5𝑥+9 Slope: 5 3 y-int: 3 D. 𝑦=8 Slope: 0 y-int: 8

Write the Equation of the Line A. Slope: −2 y-int: −4 𝑦=−2𝑥−4 B. Slope: 1 y-int: 7 𝑦=𝑥+7 C. Slope: 2 Point: (2,2) 2=2(2)+𝑏 2=4+𝑏 −2=𝑏 𝑦=2𝑥−2

Write the Equation of the Line D. Slope: −4 Point: (1,5) 5=−4 1 +𝑏 5=−4+𝑏 9=𝑏 𝑦=−4𝑥+9 E. Point: −3,7 Point: (0,4) 𝑦=−1𝑥+𝑏 𝑚= 4−7 0−(−3) 4=−1(0)+𝑏 4=𝑏 𝑚= −3 3 =−1 𝑦=−𝑥+4

Rate of Change 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 𝑚= 80−20 4−2 = 60 2 =30 Find the average rate of change of 𝑓 𝑥 =5 𝑥 2 over the interval 2,4 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 Plug in the two values for 𝑥 and solve. (𝑥=2 𝑎𝑛𝑑 𝑥=4) 5 2 2 =20  (2,20) 5 4 2 =80  (4,80) 𝑚= 80−20 4−2 = 60 2 =30

Rate of Change 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 𝑚= 56−28 16−4 = 28 12 = 7 3 Find the average rate of change of 𝑓 𝑥 =14 𝑥 over the interval 4,16 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 Plug in the two values for 𝑥 and solve. (𝑥=4 𝑎𝑛𝑑 𝑥=16) 14 4 =28  (4,28) 14 16 =56  (16,56) 𝑚= 56−28 16−4 = 28 12 = 7 3

Graph Linear Equations (and their inverse) 𝑦=3𝑥−6 3 𝑜𝑟 3 1 Slope: y-int: −6 Inverse: 𝑥=3𝑦−6 +6 +6 𝑥+6=3𝑦 𝑥 3 + 6 3 = 3𝑦 3 1 3 𝑥+2=𝑦

Find the Inverse A. 𝑦=4𝑥−2 B. 𝑦= 𝑥 5 +8 𝑥= 𝑦 5 +8 𝑥=4𝑦−2 +2 +2 −8 −8 +2 +2 −8 −8 𝑥+2=4𝑦 𝑥−8= 𝑦 5 𝑥 4 + 2 4 = 4𝑦 4 5(𝑥−8)= 𝑦 5 ∗5 𝑥 4 + 1 2 =𝑦 5𝑥−40=𝑦