CPhill

We have the points   (0, 15)  and  ( 150, 0 )

Slope  =  [  0 - 15  ]  / [ 150 - 0 ]  =   -15 / 150   =  - 1 / 10

Equation using  ( 0 , 15)

y  = (-1/10) ( x - 0) + 15

y = (-1/10) x + 15     multiply  through by -10

-10y = x - 150     add 10y to both sides

0  = x + 10y - 150

1x + 10y - 150  =  0    ⇒  Standard Form

x^2  - 5x  - 8  = 0    add 8 to both sides

x^2  - 5x   = 8

Take  1/2 of 5  = 5/2....square it  = 25/4    .....add to both sides

x^2 - 5x  + 25/4  =  8 + 25/4       factor the left side, simpliify the right

(x - 5/2)^2  =  57/4      take both roots

x - 5/2  =  ± √ [ 57 / 4 ]

x - 5/2  = ± √57 / 2      add 5/2 to both sides

x  = 5/2  + √57/ 2          or   x  =  5/2   - √57 / 2

We  have the points  (0, 56)  and (1,70)

We want to work to the form  Ax  + By  + C  =  0

Slope  =  [ 70 - 56 ]  [ 1, 0 ] =  14 / 1  = 14

Using the point  (0, 56)  we have

y  = 14 (x - 0) + 56

y  = 14x + 56    subtract  y from both sides

14x - y + 56  = 0

14x - 1y +  56  =  0

Accumulatedl amount  =  P ( 1 + r/4)^(n *t)

P = 32000

r = 3%  = .03

n = number of compoundings per year  =  4

t = number of years  = 7

32000 ( 1 + 03 / 4)^28  = 

39,446.78

80 (1.25)^10  ≈

745  books at the end of the 10th month

Slope  =  [ 5 - 15 ] / [ 0 - 2 ]  =  -10  / -2   =  5

Using   (0,5)   we have

y  =  m ( x - x1)  + y1           where m is the slope  and (x1, y1)  = ( 0, 5)

y = 5 (x - 0)  + 5   

y = 5x + 5    in slope-intercept form

Reading  at the top from left to right

The first, third and fourth equations are growth

All the rest are decay

Population in 2023  =

4600 ( 1 - .017)^7   ≈ 

4080

(1,4), (-1,2) 

First....find the slope between these two points

[2 - 4 ]  / [ -1 - 1 ]  =     -2 / -2   = 1

Using either point  - I'll use  (1, 4)  - to write the equation, we have

y  =  1 ( x - 1)  +  4

y  =  x  - 1 + 4

y  = x + 3    in slope-intercept form

Population in 2006  =

440 (1.17)^6  ≈

1129  coyotes in 2006