Suppose that the water level at the river is 45 feet after three days of no rain in 10 feet after 10 days of no rain in River with 60 feet before the job again right in equation in standard form
Let x be the number of days of no rain.
The water level after x days of no rain can be represented by the equation 60 - (x/10)*15 = y.
Therefore, the equation in standard form is 10*(60 - 15x/10) - 45 = 0.
Thus, the equation in standard form is 600 - 15x - 450 = 0.
Simplifying the equation, we get -15x + 150 = 0.
Therefore, in standard form, the equation is -15x + 150 = 0.
To determine the equation in standard form, we'll need two points on the line. Let's choose the points (3, 45) and (10, 10), where the x-coordinate represents the number of days with no rain, and the y-coordinate represents the water level in feet.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values, we have:
m = (10 - 45) / (10 - 3)
m = -35 / 7
m = -5
The slope is -5.
Now, we can substitute the slope (m) and one of the points (x1, y1) into the point-slope form of the equation:
y - y1 = m(x - x1)
Using the point (3, 45), we have:
y - 45 = -5(x - 3)
Expanding, we get:
y - 45 = -5x + 15
Next, let's rewrite the equation in standard form, Ax + By = C.
Adding 5x to both sides:
5x + y - 45 = 15
Rearranging the terms:
5x + y = 60
Therefore, the equation in standard form is 5x + y = 60.
To solve this problem, let's break it down step by step:
Step 1: Identify the given information:
- Water level at the river after three days of no rain = 45 feet
- Water level at the river after ten days of no rain = 10 feet
- Water level before the dry spell = 60 feet
Step 2: Formulate an equation using the given information:
Let's assume that the water level decreases linearly with time when there is no rain. We can use the slope-intercept form of a linear equation, which is y = mx + b, where:
- y represents the water level at a given time (in feet)
- x represents the number of days with no rain
- m represents the rate of decrease in water level per day
- b represents the y-intercept, which is the water level before the dry spell
Step 3: Calculate the rate of decrease (m):
To find the rate of decrease, we need to calculate the change in water level per day. We can use the formula:
Change in y / Change in x = (y2 - y1) / (x2 - x1)
Using the given information:
- y1 = 45 feet (water level after three days of no rain)
- y2 = 10 feet (water level after ten days of no rain)
- x1 = 3 days
- x2 = 10 days
Substituting these values into the formula:
(m) = (10 - 45) / (10 - 3)
(m) = -35 / 7
(m) = -5
So, the rate of decrease in water level is 5 feet per day.
Step 4: Substitute the values into the equation:
Now that we know the rate of decrease (m) and the y-intercept (b), we can substitute these values into the equation and rewrite it in standard form (ax + by = c):
Using the known values:
m = -5
b = 60
The equation becomes:
-5x + y = 60
Converting it to standard form, we multiply the entire equation by -1 to make the coefficient of x positive:
5x - y = -60
Therefore, the equation in standard form is 5x - y = -60.