Question

apply your knowledge of slope - intercept form to answ

1. mia has $50 on a gift card to her favorite

coffee shop. each time she visits the coffee
shop she spends $3.75 on her favorite drink.
write an equation to represent the relationship
between n, the number of times she visits the
coffee shop, and b, the total balance on her
gift card.
robert pays for his family to go to the arcade. he pays
additional amount per game that his family plays as sho

Explanation:

Step1: Identify the initial value and rate of change

The initial balance on the gift card (when \( n = 0 \), no visits) is \( \$50 \), so this is the y - intercept (\( b_0 \)) in the slope - intercept form \( y=mx + b \) (here our variables are \( b \) (balance) and \( n \) (number of visits), so the equation will be \( b=mn + b_0 \)). The rate of change is the amount spent per visit, which is \( -\$3.75 \) (negative because the balance is decreasing) per visit. So the slope (\( m \)) is \( - 3.75 \) and the y - intercept (\( b_0 \)) is \( 50 \).

Step2: Write the equation

Using the slope - intercept form \( b=mn + b_0 \), substitute \( m=-3.75 \) and \( b_0 = 50 \). We get the equation \( b=-3.75n + 50 \).

Answer:

\( b=-3.75n + 50 \)