Question

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?

Answer 1

To calculate the cost of a health club membership based on month length, use the linear equation c = 20m + 20, where m represents the number of months. A 30-month membership costs $620.

Step-by-step explanation:

To find the equation that can be used to calculate the cost of a 30-month health club membership, we use the information that the relationship is linear. First, we identify two points: (12, 260) and (18, 380), where the first number is the months, and the second number is the cost. Using the formula for the slope of a line (m = (y2 - y1) / (x2 - x1)), we calculate the slope to determine the rate at which the cost increases per month. The slope (m) is (380 - 260) / (18 - 12) = 120 / 6 = 20. This means the cost increases by $20 for each additional month.

Now that we know the slope, we can use one of the points to find the y-intercept (b) of the equation c = m*m + b. Substituting the point (12, 260) into the equation gives us 260 = 20*12 + b, which simplifies to 260 = 240 + b, so b = 260 - 240 = $20. The linear equation that represents the cost for any length of membership in months is then c = 20m + 20.

To find the cost of a 30-month membership, we substitute m = 30 into the equation: c = 20*30 + 20, which gives us c = 600 + 20 = $620. Thus, the cost of a 30-month membership is $620.

Answer 2

(12,260)(18,380)
slope = (380 - 260) / (18 - 12) = 120/6 = 20

y = mx + b
slope(m) = 20
(12,260)...x = 12 and y = 260
now we sub and find b, the y int
260 = 20(12) + b
260 = 240 + b
260 - 240 = b
20 = b

ur equation for the line is y = 20x + 20

the cost of a 30 month membership..
y = 20(30) + 20
y = 600 + 20
y = 620

so basically, ur equation (with ur variables) is :
c = 20m + 20......and for 30 months, sub in 30 for m
c = 20(30) + 20