Question

angelo's mother put $50 on a lunch card he spends the same amount each day for lunch. what is the constant rate of change for this function. choose two ordered pairs and write a ratio that can be used to find the slope or constant rate of change.

Answer 1

Given that Angelo spends the same amount everyday from the amount in

the lunch card, the function of the amount remaining is a linear function.

• The constant rate of change of the function is; -5.25

• The two ordered pair used to find the constant rate of change are; (1, 44.75) and (2, 39.5)

Reasons:

The amount Angelo's mother put on the lunch card = $50

A possible table of values to the question is presented as follows;

$\begin{tabular}{r|c|c|c|c|}Days&0&1&2&3\\Money Remaining&&44.75&39.5&\end{array}\right]$

Required:

The constant rate of the function that gives the amount remaining from the

amount Angelo's mother put on his lunch card.

Solution:

• $Slope \ or \ constant \ rate \ of \ change = \mathbf{\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}$

The two ordered pair that can be used to find the slope or constant rate of change are;

(x₁, y₁) = (1, 44.75), and (x₂, y₂) = (2, 39.5)

With the above two ordered pairs, we have the constant rate of change of the function given as follows;

$Constant \ rate \ of \ change\ (The \ slope) =\dfrac{39.5-44.75}{2-1} = \mathbf{ -5.25}$

The constant rate of change for the function that gives the amount remaining in the lunch card is; -5.25

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