ANSWER
The equation is
[tex]y-20=\frac{10}{3}(x-6)[/tex].
EXPLANATION
The point-slope form the equation of a straight line is given by the formula,
[tex]y-y_1=m(x-x_1)[/tex].
where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is any point on the line.
We were given that the rate of change for the situation is [tex]\frac{10}{3}[/tex].
Since the rate represents the slope, [tex]m=\frac{10}{3}[/tex].
We were again told that at day 6 of the month, she spent $[tex]20[/tex].
This implies that [tex](x_1=6,y_1=20)[/tex]. 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,
[tex]y-20=\frac{10}{3}(x-6)[/tex]
