Answer:
To write the equation in function form for the number of calls in each week by the mechanic, we can use the concept of linear reduction.
Let's assume:
- Week 3 as the starting week (x = 0).
- Week 13 as the ending week (x = 10).
We have two data points:
- (x1, y1) = (0, 391) (week 3, number of calls fixed in week 3)
- (x2, y2) = (10, 361) (week 13, number of calls fixed in week 13)
We can use these two points to determine the equation of a straight line in the form y = mx + b, where m is the slope and b is the y-intercept.
First, calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
= (361 - 391) / (10 - 0)
= -3
Next, substitute the slope (m) and one of the data points (x1, y1) into the equation y = mx + b to find the y-intercept (b):
391 = -3(0) + b
b = 391
Therefore, the equation in function form to show the number of calls in each week by the mechanic is:
y = -3x + 391
Where:
- y represents the number of calls in each week fixed by the mechanic.
- x represents the week number, starting from week 3 (x = 0) and ending at week 13 (x = 10).