Final answer:
To find the equation representing the monthly cost of the Splint plan, we use the slope-intercept form of a linear equation. The equation is y = 0.49x + 16.15. When 625 minutes are used, the total monthly cost will be $322.4.
Step-by-step explanation:
To find the equation representing the monthly cost of the Splint plan, we can use the slope-intercept form of a linear equation, which is y = mx + b. Here, y represents the total monthly cost and x represents the number of monthly minutes used. To find the equation, we need to determine the values of m (slope) and b (y-intercept).
We are given two data points: (370 minutes, $193.5) and (750 minutes, $364.5).
Using the slope formula, we can find the slope:
- Let x1 = 370, y1 = 193.5, x2 = 750, and y2 = 364.5
- Slope (m) = (y2 - y1) / (x2 - x1) = (364.5 - 193.5) / (750 - 370) = 0.49
Now, let's substitute one of the data points (370 minutes, $193.5) into the equation:
- x = 370 and y = 193.5
- 193.5 = 0.49 * 370 + b
- b = 193.5 - 0.49 * 370 = 16.15
Therefore, the equation representing the monthly cost of the Splint plan is y = 0.49x + 16.15.
To find the total monthly cost when 625 minutes are used, we can substitute x = 625 into the equation:
- x = 625
- y = 0.49 * 625 + 16.15
- y = 306.25 + 16.15 = $322.4 (rounding to the nearest cent)
So, if 625 minutes are used, the total cost will be $322.4.