Absolutely, let's work through this step by step.
### Crocodile River
To determine the equation of the Crocodile River in slope-intercept form (y = mx + b), let's follow these steps:
1. Identify the given points: We are given two points through which the Crocodile River passes: (1, 2) and (3, 4).
2. Calculate the slope (m):
[tex]\[
\text{slope} = m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 2}{3 - 1} = \frac{2}{2} = 1.0
\][/tex]
3. Determine the y-intercept (b):
Using the slope-intercept form y = mx + b, we can substitute one of the points (let's use (1, 2)) and the slope to solve for b.
[tex]\[
2 = (1.0) \cdot 1 + b \implies 2 = 1.0 + b \implies b = 2 - 1.0 = 1.0
\][/tex]
4. Write the equation:
Thus, the equation of the Crocodile River is:
[tex]\[
y = 1.0x + 1.0
\][/tex]
### Serengeti Stream
To determine the equation of the Serengeti Stream in slope-intercept form, let’s proceed similarly:
1. Identify the given points: We are given two points through which the Serengeti Stream passes: (2, 3) and (4, 7).
2. Calculate the slope (m):
[tex]\[
\text{slope} = m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2.0
\][/tex]
3. Determine the y-intercept (b):
Using the slope-intercept form y = mx + b, we can substitute one of the points (let’s use (2, 3)) and the slope to solve for b:
[tex]\[
3 = (2.0) \cdot 2 + b \implies 3 = 4.0 + b \implies b = 3 - 4.0 = -1.0
\][/tex]
4. Write the equation:
Thus, the equation of the Serengeti Stream is:
[tex]\[
y = 2.0x - 1.0
\][/tex]
### Summary
- Crocodile River: [tex]\(y = 1.0x + 1.0\)[/tex]
- Serengeti Stream: [tex]\(y = 2.0x - 1.0\)[/tex]
These steps ensure that we have accurately modeled each body of water using linear equations in slope-intercept form.
