13. Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no rain. The river was 60 feet before the drought began.(4 points)

Question

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a. What is the rate of change (slope) for this scenario? 5

b. What is the y-intercept for this scenario? (0, 60)

c. Write an equation for the scenario in slope-intercept form. y=5x+45
𝑦
=
5
𝑥
+
45

d. Write an equation in standard form. 5x+y=60
5
𝑥
+
𝑦
=
60

(-5, 0)155x+y=35
5
𝑥
+
𝑦
=
35
y=−5x−35
𝑦
=
−
5
𝑥
−
35
-5(0, -5)−5x+y=60
−
5
𝑥
+
𝑦
=
60
y=−5x+60
𝑦
=
−
5
𝑥
+
60
Question 2
14. Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no rain. Given the two points we …

Answer 1

To address the problem step by step, we need to analyze the information given.

Given Data:

1. Water Level at Day 3: 45 feet
2. Water Level at Day 10: 10 feet
3. Initial Water Level (Before Drought): 60 feet

a. Rate of Change (Slope)

The slope or rate of change can be calculated using the formula:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

Let (x₁, y₁) = (3, 45) and (x₂, y₂) = (10, 10):

\[ \text{slope} = \frac{10 - 45}{10 - 3} = \frac{-35}{7} = -5 \]

The rate of change (slope) is -5.

b. Y-Intercept

The y-intercept occurs when x = 0. The river's initial level before the drought began was 60 feet when no time has passed. Thus, the y-intercept is also (0, 60).

c. An Equation in Slope-Intercept Form

Using the slope-intercept form, \(y = mx + b\), we can substitute the slope (-5) and y-intercept (60):

Substituting into the equation:

\[ y = -5x + 60 \]

d. An Equation in Standard Form

To rewrite the equation in standard form \(Ax + By = C\):

Starting from \(y = -5x + 60\):

1. Add \(5x\) to both sides:

\[ 5x + y = 60 \]

So the standard form is 5x + y = 60.

Summary of Responses:

• a. Rate of change (slope): -5
• b. Y-Intercept: (0, 60)
• c. Equation in slope-intercept form: \(y = -5x + 60\)
• d. Equation in standard form: \(5x + y = 60\)

If you have further questions or need clarifications on other parts of the scenario, let me know!