Question

nevaeh uses a gift card to buy a cup of coffee every morning. the table shows the amount of money left on the card, y, as a function of the number of cups of coffee she buys, x. find and describe the rate of change of the function. the rate of change is -3. it represents a decrease in the amount on the gift card for every cup nevaeh purchases. find and describe the initial value of the function. the initial value is

Explanation:

Step1: Find the slope - intercept form equation

The rate of change (slope $m$) is - 3. The equation of a line is $y=mx + b$, where $x$ is the number of cups, $y$ is the amount on the card, $m$ is the slope and $b$ is the initial value. We can use a point from the table, say $(x = 2,y = 19)$. Substitute into $y=-3x + b$.

Step2: Solve for $b$

$19=-3\times2 + b$.
$19=-6 + b$.
Add 6 to both sides: $b=19 + 6=25$.

Answer:

25