After six hours of rainfall today, Yvette recorded the amount of rain in inches y in a rain gauge the table, shows the linear relationship for the recorded rainfall
Rain gauge
Time X hours 3 4 5
Amount of rain and gauge, Y inches 3. 75. 4.5 5.25
How many inches of rain was in the gauge before the rain began today and what was the rate at which the rain fell in inches per hour?
To find out how many inches of rain were in the gauge before the rain began, we can use the equation Y = mx + b, where Y is the amount of rain in the gauge, x is the time in hours, m is the rate at which the rain fell in inches per hour, and b is the initial amount of rain in the gauge before the rain began.
Using the data provided in the table, we can plug in the values for x and Y:
When x = 3, Y = 3 inches
When x = 4, Y = 3.75 inches
When x = 5, Y = 4.5 inches
Now we can set up a system of equations to solve for b and m:
3 = 3m + b
3.75 = 4m + b
4.5 = 5m + b
Subtracting the first equation from the second and third equations, we get:
0.75 = m
1.5 = 2m
Now we can plug in m = 0.75 into the first equation to solve for b:
3 = 3(0.75) + b
3 = 2.25 + b
b = 0.75
Therefore, there were 0.75 inches of rain in the gauge before the rain began today, and the rate at which the rain fell was 0.75 inches per hour.