Question

how should she write a point slope equation to represent her parking cost after a given number of days?

Answer 1

The equation is

`y-20=(10)/(3)(x-6)`.

Step-by-step explanation

The point-slope form the equation of a straight line is given by the formula,

`y-y_1=m(x-x_1)`.

where
`m` is the slope and
`(x_1,y_1)` is any point on the line.

We were given that the rate of change for the situation is
`(10)/(3)`.

Since the rate represents the slope,
`m=(10)/(3)`.

We were again told that at day 6 of the month, she spent $
`20`.

This implies that
`(x_1=6,y_1=20)`. Note that the cost depends on the number of days. Hence the number of days is the independent variable.

We can now substitute in to the formula to obtain,

`y-20=(10)/(3)(x-6)`