Lucy has a budget for school stationery of 33, but has already spent 22.47 on books and folders. Let p represent the amount that Lucy can spend on other stationery. Write an inequality that shows how much she can spend on other stationery, and solve for p.

The inequality is;

p≤ 10.53

where 10.53 is the highest value she can spend on other stationery

Step-by-step explanation:

Here, we want to write an inequality

The amount she has to spend is 33

This means she can spend less than or equal to this amount

she has spent 22.47 and still has p to spend

Mathematically;

p + 22.47 ≤ 33

p ≤ 33-22.47

p ≤ 10.53

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: