Question

north shore kayak and south shore kayak each charge a flat fee plus an hourly rate. the graph shows y, the cost in dollars, for renting a kayak from each company for x hours. kayak rental graph omitted which statement about the companies is true? show hints the companies have the same hourly rate. south shore costs more when renting a kayak for 2 hours. the flat fee is higher for north shore than for south shore. the companies cost the same when renting a kayak for 1 hour.

Explanation:

Step1: Analyze the hourly rate (slope)

For North Shore, the equation is \( y = 12x + 4 \), so the hourly rate (slope) is \( 12 \) dollars per hour. For South Shore, the equation is \( y = 6x + 10 \), so the hourly rate (slope) is \( 6 \) dollars per hour. So the first option is false.

Step2: Calculate cost for 2 hours

For North Shore: \( y = 12(2) + 4 = 24 + 4 = 28 \) dollars. For South Shore: \( y = 6(2) + 10 = 12 + 10 = 22 \) dollars. So South Shore costs less for 2 hours, second option is false.

Step3: Analyze the flat fee (y-intercept)

For North Shore, the flat fee (y-intercept) is \( 4 \) dollars. For South Shore, the flat fee (y-intercept) is \( 10 \) dollars. So North Shore's flat fee is lower, third option is false.

Step4: Calculate cost for 1 hour

For North Shore: \( y = 12(1) + 4 = 16 \) dollars. For South Shore: \( y = 6(1) + 10 = 16 \) dollars. So both companies cost the same for 1 hour, fourth option is true.

Answer:

The companies cost the same when renting a kayak for 1 hour.