The graph below shows the height of a snowman over time Writ

The graph below shows the height of a snowman over time. Write a function rule. What is the initial height (y-intercept) of the snowman? What is the rate of change (slope) of his height over time? Mrs. Savin receives a weekly base salary of $500, plus a commission of $1,200 on each car that she sells. Write a function rule relating her total weekly pay p to cars she sells c. What are the initial value (y-intercept) and rate of change (slope)?

Solution

3)

we can see that initial height (at time =0) is 9 feets           (from graph) (y-intercept)

slope (rate of change) = change in height /change in time       (vertical change/ horizontal change)

                                    =   (9-5.5)/(0-7) = 3.5/-7 = -1/2

the equation of a straight line is y = mx +b

      here y = height . m=slope , x= time and b = y-intercept

            Height    =   (-1/2) * x + 9     

.

savin base salary = $ 500

commision on car = $1200

number of cars she sells in a week = c

therefore total commision in a weak = 1200*c

total salary = base salary + total commision

p = 500 +1200c

p = 1200c + 500

comparing with slope -intercept form of a line

y = mx + b

we get m(slope) = 1200

b(y-intercept or inital value) = 500