Question

Suppose that the water level of a river is 34 feet after three days of rain and 62 feet after 10 days of rain given two points we know three 3410, 62. What would the slope equation look like?

Answer 1

To find the slope equation of the line that represents the relationship between the days of rain and the water level of the river, we can use the two points provided: (3, 34) and (10, 62).

1. **Identify the points:**
- Point 1: \( (x_1, y_1) = (3, 34) \)
- Point 2: \( (x_2, y_2) = (10, 62) \)

2. **Calculate the slope (m):**
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the values:
\[
m = \frac{62 - 34}{10 - 3} = \frac{28}{7} = 4
\]

3. **Form the equation of the line:**
We can use the point-slope form of the equation of a line, which is:
\[
y - y_1 = m(x - x_1)
\]
Using point (3, 34) and the calculated slope, we have:
\[
y - 34 = 4(x - 3)
\]

4. **Simplify the equation:**
Expanding the equation:
\[
y - 34 = 4x - 12
\]
Adding 34 to both sides:
\[
y = 4x + 22
\]

Thus, the slope equation that represents the water level in relation to the days of rain is:
\[
y = 4x + 22
\]

Where \( y \) is the water level in feet and \( x \) is the number of days of rain.