1. Rate of change and slope
2.3
Rate of change and slope

2. Rate of change = rise / run
r= rise/run
r= d/t r d t
Rate of change =
Change in y /change in x Or
Rate of change =Δy/Δx
Rate of change = rise / run

3. where m is the slope Slope of a line Δy Δx
The slope of the line is the ratio of the change in y-coordinates to the change in the x- coordinates OR
m =( y2 – y1 ) / ( x2 – x1 )
where m is the slope Δy Δx

4. Example : # 14 pg 80
Find the slope of the line passing through the following points : ( -1.5 , 3.5 ) and ( 4.5 , 6) m=( y2 – y1 ) / ( x2 - x 1 ) m = = 5/ 12

5. Determine the rate of change of each graph:
( 1,5), (-1 , 1)
m= (1-5) /( ) = -4 / -2
m = 2 Δy Δx

6. ( -1 , 8 ) and ( 2 , 2 )
m= ( 2 – 8 )/(2 – (-1 ))
m = -6 / 3
m= -2

7. The slope of the horizontal line is zero
m = o/ 2 or 0/5
m = 0
There is run but No rise

8. The slope of the vertical line is undefined
m = 5/ 0 or
7 / 0
m is undefined

9. Dealing with lines Slope is - ve Slope is + ve Slope is zero
Slope is undefined
Slope is zero

10. To find the slope from a given equation, This equation should be in the form of y = m x + b
Example :
Find the rate of change for each equation
6y = 8x – ( ÷ 2 )
3y = 4x ( ÷ 3 )
y = 4/3 x – 20/3
m = 4/3

11. 2 ) -2y -16 x = y = 16 x + 41 y = -8x – 41/ 2 m = - 8 3) 12 x – 4y + 5 =18 12 x – 4y = x – 13 = 4 y ( ÷ 4 ) 3 x – 13 / 4 = y m = 3
( ÷ - 2 )

12. 4 )
Multiply each term by 4
6x – 5 y = 60
6 x – 60 = 5 y
6/5 x = y
m = 6/5

13. Unknown value (10,r) ,(4,3) , m = 4/3 r= 11
Find the value of r that the line passes through each pair of points has the given slope.
(10,r) ,(4,3) , m = 4/3
m =( y2 – y1 ) / ( x2 – x1 )
m= (3-r)/(4-10) = ( 3 – r ) / - 6
r= 11

14. Thank you Required exercises are :
3, 9, 10, 11(a, b, c), 12 to 21, 23 to 28, 31 to 34, 36, 37, 40(a, b, c), 41, 42, 43, 44.
Pages : 79-82
Thank you