Suppose that the water level of a river is 45 feet after three days of no rain in 10 feet after 10 days and no rain the river with 60 feet before the job again right in equation for the scenario in slope intercept form
To write the equation in slope-intercept form (y = mx + b), we need to determine the values of m (slope) and b (y-intercept).
Given:
After 3 days of no rain:
Water level = 45 feet
After 10 days of no rain:
Water level = 10 feet
Before the river fills again:
Water level = 60 feet
We can consider the number of days as the x-values and the water level as the y-values.
Using the slope formula, we can determine the slope (m):
m = (change in y) / (change in x)
change in y = 45 - 10 = 35
change in x = 3 - 10 = -7
m = 35 / (-7) = -5
Now, let's consider the point (10, 60) to find the y-intercept (b).
y = mx + b
60 = -5(10) + b
60 = -50 + b
b = 60 + 50
b = 110
Therefore, the equation in slope-intercept form is:
y = -5x + 110
To find the equation in slope-intercept form, we need to identify the slope and y-intercept.
Let's denote the number of days as x and the water level as y.
From the given information, we can find two data points:
(3, 45) and (10, 10).
To find the slope (m), we can use the formula: m = (y2 - y1) / (x2 - x1).
Using the points (3, 45) and (10, 10), we have:
m = (10 - 45) / (10 - 3).
m = -35 / 7.
m = -5.
Now that we have the slope, we can determine the y-intercept (b) using the formula: b = y - mx.
Using the point (3, 45), we have:
45 = -5(3) + b.
45 = -15 + b.
b = 60.
Therefore, the equation in slope-intercept form is:
y = -5x + 60.
To write an equation in slope-intercept form, we need to find the slope (m) and the y-intercept (b) for the given scenario.
In this case, we have three data points:
- Day 3: water level = 45 feet
- Day 10: water level = 10 feet
- Before the job: water level = 60 feet
Let's first find the slope (m) using the formula:
m = (Change in y) / (Change in x)
Change in y = 10 - 45 = -35
Change in x = 10 - 3 = 7
So, m = -35/7 = -5
Now, let's find the y-intercept (b). We have the point (10, 10) on the line, so we can use it to solve for b.
Using the point-slope formula:
y - y1 = m(x - x1)
Substituting the known values:
y - 10 = -5(x - 10)
Expanding the equation:
y - 10 = -5x + 50
Rearranging the equation to slope-intercept form (y = mx + b):
y = -5x + 60
Therefore, the equation for this scenario in slope-intercept form is y = -5x + 60.