Final answer:
The slope of the cost for Ivy's Lawn Care Service is $0.50 per minute, and the y-intercept is $30, representing the initial service charge.
Step-by-step explanation:
To find the slope and y-intercept of Ivy's Lawn Care Service's pricing structure, we need to understand that the cost depends on the number of minutes of service.
Step 1: Identify two points
Let's use the given data to identify two points on this linear relationship: (15, 37.50) and (20, 40.00).
Here, '15' and '20' represent the minutes, while '37.50' and '40.00' represent the cost in dollars.
Step 2: Calculate the slope
The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).
Plugging in the values from our points, we get m = (40.00 - 37.50) / (20 - 15) = 2.50 / 5 = 0.50. So, the slope is 0.50 dollars per minute.
Step 3: Find the y-intercept
To find the y-intercept (b), we can plug in the slope and one pair of points into the formula y = mx + b and solve for b. Using the point (15, 37.50), we have 37.50 = 0.50(15) + b.
Solving for b gives us b = 37.50 - 7.50 = 30. Therefore, the y-intercept is $30.