12. 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)Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.a. What is the rate of change (slope) for this scenario? Response areab. What is the y-intercept for this scenario? Response area c. Write an equation for the scenario in slope-intercept form. Response aread. Write this equation in standard form. Response areay=28x+34(0,22)y=4x+340(0,4)y=4x−22y=4x+224x+y=344−4x+y=34728(0,34)22(0,0)−4x+y=22

Answer 1

To analyze this scenario, let's first identify the information provided and then calculate the requested values step-by-step.

1. Given data:

   • Water level at 3 days: 34 feet
   • Water level at 10 days: 62 feet
   • Initial water level before rain began: 22 feet

2. Calculate the rate of change (slope):

   • The slope (rate of change) can be calculated using the formula:

     \[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \] where \( (x_1, y_1) = (3, 34) \) and \( (x_2, y_2) = (10, 62) \).

   • Plugging in the values:

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

   Response for part (a): The rate of change (slope) is 4.

3. Determine the y-intercept:

   • We know that the water level before the rain began is 22 feet. This indicates that at \( x = 0 \) (before the rain), the water level was 22 feet.

   Response for part (b): The y-intercept is 22.

4. Write the equation in slope-intercept form:

   • The slope-intercept form is given by:

     \[ y = mx + b \]

   • Using the slope \( m = 4 \) and the y-intercept \( b = 22 \):

     \[ y = 4x + 22 \]

   Response for part (c): The equation in slope-intercept form is y = 4x + 22.

5. Convert this equation to standard form:

   • The standard form of a linear equation is \( Ax + By = C \). Rearranging our slope-intercept form \( y = 4x + 22 \):

     \[ -4x + y = 22 \] or, to follow the convention of having \( A \) as a positive integer:

     \[ 4x - y = -22 \]

   Response for part (d): The equation in standard form is 4x - y = -22.

So the complete responses for each part are:

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