Question

name: parker
final exam review worksheet

1. emaan charges a fixed amount for a bracelet, with an additional charge for each charm

a customer adds to the bracelet. write a linear function f that emaan can use to find the
price of a bracelet.

charms	5	10	20	30

what is the fixed cost of a bracelet?
what is the price per charm?
write a linear function in function notation to represent the situation.

Explanation:

Step1: Find the slope (price per charm)

The slope \( m \) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using points \((5, 110)\) and \((10, 180)\):
\( m=\frac{180 - 110}{10 - 5}=\frac{70}{5}=14 \). So price per charm is \( \$14 \).

Step2: Find the fixed cost (y-intercept)

Use the linear equation \( y = mx + b \), where \( y \) is cost, \( x \) is charms, \( m = 14 \), and plug in \((5, 110)\):
\( 110 = 14(5)+b \)
\( 110 = 70 + b \)
\( b = 110 - 70 = 40 \). So fixed cost is \( \$40 \).

Step3: Write the linear function

The linear function is \( f(x)=mx + b \), so \( f(x)=14x + 40 \), where \( x \) is the number of charms.

Answer:

• Fixed cost of a bracelet: \(\$40\)
• Price per charm: \(\$14\)
• Linear function: \( f(x) = 14x + 40 \)