Question

Hellen used a coupon she received in the mail at a local boutique that decreased her purchase of $85.20 by $12.78. Her sister used the same coupon and decreased her purchase of $63.80 by $9.57. Write the equation of a line, in the form y = mx + b, to model this linear relationship.

Answer 1

y = 12665 (100⁻¹) + b

Explanation:

To model this relationship, you're to write the equation of a line; in the form

y = mx + b

Now let y represent the full coupon value,

mx represent the amount spent by Hellen and her sister

and b, the change that's left on the coupon.

So, the summary of Hellen's transaction is:

$85.2 became $(85.2 - 12.78) which is = $72.42

The summary of her sister's transaction is:

$63.8 became $(63.8 - 9.57) which is = $54.23

So y - (72.42 + 54.23) = b

y - 126.65 = b

y = 126.65 + b

Separating m from x in mx, you have

y = 12665 x 1/100 + b

y = 12665 (100⁻¹) + b

Where m = 12,665 and x = 100⁻¹