Question

What is the equation that represents Eric’s gift card balance, where x represents the time and y represents the balance?

Enter your answers in the boxes.

Answer 1

`y - 100 = \boxed{\:-(25)/(2) \:} \;\;\left(x -\boxed{\:4\:}\:\right)`

Explanation:

The first thing to observe is that the balance declines at a linear rate with respect to time in weeks

The given equation which you have to fill in is in the point-slope form of a straight line

The point slope equation of a straight line is
y - y1 = m(x - x1)

where (x1, y1) is a point on the line
m is the slope = (x2 - x1)/(y2 - y1) with (x1, y1) and (x2, y2) being two points on the line

To find the slope,

Let's take two points say 4, 100) and (8,50) where the first entry is the weeks and second is the current balance

Slope m = (50 - 100)/(8 - 4) = - 50/4 = -25/2

The negative value simply indicates that the balance is declining by 25/2 every two weeks

Having got the slope we can rewrite the equation as

y - y1 = -25/2(x - x1)

Again take (x1, y1) as (4, 100) to get

`y - 100 = \boxed{-(25)/(2)} (x -\boxed{ 4})`

And this is the answer