1. **Stating the problem:** We have three health clubs with different payment plans: - Club A: Initial fee $150, monthly fee $45 - Club B: Initial fee $250, monthly fee $35 - Club C: No initial fee, monthly fee $60 We need to identify which table corresponds to which club, write equations for each club's cost over time, explain slope and y-intercept, and determine which club each friend should join to minimize cost. 2. **Identify each club's table:** - Club C has no initial fee, so at 0 months cost should be $0, but table shows $60 at 0 months, so this must be a mistake in the problem statement or table. However, given the monthly cost is $60, the table with cost increasing by $60 each month and starting at $60 is Club C. - Club A has initial fee $150 and $45 per month. Check table with first month cost $195: $150 + $45*1 = $195 matches Club A. - Club B has initial fee $250 and $35 per month. Check table with first month cost $285: $250 + $35*1 = $285 matches Club B. So: - Table with costs 60,120,180,... is Club C - Table with costs 195,240,285,... is Club A - Table with costs 285,320,355,... is Club B 3. **Write equations for each club:** General form: $$y = mx + b$$ where $y$ is total cost, $m$ is monthly fee (slope), $x$ is months, and $b$ is initial fee (y-intercept). - Club C: Initial fee $0$, monthly fee $60 $$y = 60x + 0 = 60x$$ - Club A: Initial fee $150$, monthly fee $45 $$y = 45x + 150$$ - Club B: Initial fee $250$, monthly fee $35 $$y = 35x + 250$$ 4. **Explain slope and y-intercept:** - Slope ($m$) means the cost increase per month. - Y-intercept ($b$) means the initial fee paid before any months. | Club | Equation | Slope Meaning | Y-intercept Meaning | |-------|----------|---------------|---------------------| | C | $y=60x$ | $60$ dollars per month | $0$ initial fee | | A | $y=45x+150$ | $45$ dollars per month | $150$ initial fee | | B | $y=35x+250$ | $35$ dollars per month | $250$ initial fee | 5. **Determine best club for each friend:** Calculate total cost for each friend at each club. - D'juan (6 months): - Club C: $y=60*6=360$ - Club A: $y=45*6+150=270+150=420$ - Club B: $y=35*6+250=210+250=460$ Lowest cost: Club C ($360$) - Cho (10 months): - Club C: $60*10=600$ - Club A: $45*10+150=450+150=600$ - Club B: $35*10+250=350+250=600$ All cost $600$, so any club is equal cost. - Lina (12 months): - Club C: $60*12=720$ - Club A: $45*12+150=540+150=690$ - Club B: $35*12+250=420+250=670$ Lowest cost: Club B ($670$) **Final answers:** - D'juan should join Club C. - Cho can join any club (all cost the same). - Lina should join Club B.