the cost, c, of a health - club membership is related linearly to its length in months, m. if a 12 - month…

the cost, c, of a health - club membership is related linearly to its length in months, m. if a 12 - month membership costs $260 and an 18 - month membership costs $380, which equation can be used to find the cost of a 30 - month membership?\n$c - 380=\frac{1}{20}(30 - 18)$\n$c - 18 = 20(380 - 30)$\n$c - 380 = 20(30 - 18)$\n$c - 18 = 20(30 - 12)$

the cost, c, of a health - club membership is related linearly to its length in months, m. if a 12 - month membership costs $260 and an 18 - month membership costs $380, which equation can be used to find the cost of a 30 - month membership?\n$c - 380=\frac{1}{20}(30 - 18)$\n$c - 18 = 20(380 - 30)$\n$c - 380 = 20(30 - 18)$\n$c - 18 = 20(30 - 12)$

Answer

Explanation:

Step1: Find the slope of the linear relationship

The slope $m$ of a line passing through two points $(m_1,c_1)$ and $(m_2,c_2)$ is given by $m=\frac{c_2 - c_1}{m_2 - m_1}$. Here, $(m_1,c_1)=(12,260)$ and $(m_2,c_2)=(18,380)$. So, $m=\frac{380 - 260}{18 - 12}=\frac{120}{6}=20$.

Step2: Use the point - slope form of a line

The point - slope form of a line is $c - c_1=m(m - m_1)$. We can use the point $(m_1,c_1)=(18,380)$ and $m = 20$ to find the cost $c$ for $m = 30$. Substituting into the point - slope form, we get $c-380=20(30 - 18)$.

Answer:

$c - 380=20(30 - 18)$