Suppose that the water level of a river is 34 feet after 3 days of rain and 62 feet after 10 days of rain. The river was 22 feet before the rain began.(4 points)

Question

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

b. What is the y-intercept for this scenario? Response area

c. Write an equation for the scenario in slope-intercept form. Response area

d. Write this equation in standard form. Response area

28, 4, (0,22), 0, 22, (0, 4), 7, (0, 0), (0, 34), y = 4x +22, y = 4x + 34, y = 4x - 22, -4 + y = 22, 4x + y = 34, y = 28x + 34, -4x + y = 34

Answer 1

To answer the questions, we'll follow these steps:

Given Information:

• The water level after 3 days (x = 3) is 34 feet.
• The water level after 10 days (x = 10) is 62 feet.
• The water level before the rain began (when x = 0) is 22 feet.

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

To find the slope (rate of change), we can use the formula:

\[ \text{slope} (m) = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points (3, 34) and (10, 62):

\[ m = \frac{62 - 34}{10 - 3} = \frac{28}{7} = 4 \]

Response for a: 4

b. What is the y-intercept for this scenario?

The y-intercept is the value of y when x = 0. From the information given, the river was at 22 feet before the rain began.

Response for b: 22

c. Write an equation for the scenario in slope-intercept form.

The slope-intercept form is given by the equation:

\[ y = mx + b \]

Where m is the slope, and b is the y-intercept. Substituting in our values:

\[ y = 4x + 22 \]

Response for c: y = 4x + 22

d. Write this equation in standard form.

The standard form is usually expressed as \(Ax + By = C\). Starting from the slope-intercept form we derived:

\[ y = 4x + 22 \]

Rearranging this gives:

\[ -4x + y = 22 \quad \text{(which can be multiplied by -1 for a more conventional look)} \]

This yields:

\[ 4x - y = -22 \]

However, the common practice is to keep \(A\) positive, so we can leave it as:

\[ -4x + y = 22 \quad \text{(or equivalently, } 4x - y = -22 \text{)} \]

Response for d: -4x + y = 22

Summary of Responses:

• a. 4
• b. 22
• c. y = 4x + 22
• d. -4x + y = 22