The table shows the total cost to be a member of the gym for different numbers of months.
Number of months. total costs
3. $53.97
6. $77.94
12. $125.88
Create a function that gives the total cost C, in dollars to be a member of the gym given the number of months M of membership.
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Total cost = M* (factor per month ) + b
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The expression for a linear equation is
*The slope-intercept form.
y = mx + b
m= (y2-y1)/ (x2-x1) (I)
y-intercept is (0, b)
*and the point-slope form
y- y1 = m(x-x1) (II)
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Point 1 (3, 53.97)
Point 2 (12, 125.88)
Replacing in (II)
The slope m = (y2- y1)/ (x2-x1) = (125.88- 53.97)/(12-3) = 7.99
y - 53.97 = 7.99* (x- 3)
y = 7.99 x - 7.99* 3 + 53.97
y = 7.99x + 30
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Verifying
y = 7.99x + 30
x= 3
y = 7.99*3 + 30
y= 53.97
x= 6
y = 7.99*6 + 30
y= 77.94
x= 12
y = 7.99*12 + 30
y= 125.88
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Answer
The linear function is y = 7.99x + 30