1. Slope and Rate of Change

2. 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

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

4. 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 )

5. 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)

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

7. 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

8. 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

9. 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)
=20  (2,20)
=80  (4,80)
𝑚= 80−20 4−2 = 60 2 =30

10. 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)
=56  (16,56)
𝑚= 56−28 16−4 = = 7 3

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

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