Question

Week 4 - Math 8 - Assessment
3 of 11 3 of 11 Items













Question
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.
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.

What is the rate of change for this scenario? Response area

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

Write an equation in Point-slope form. Response area

Change that equation to Standard form. Response area

41/412(0, 0)(0, 22)(3, 34)(10, 62)(y - 34) = 4(x + 3)(y - 10) = 1/4(x - 62)(y - 62) = 4(x - 10)4x - y = -223x + 34y = 2210x - 62y = 22

Answer 1

To solve the problem, we need to analyze the given information about the river's water level changes over a period of time.

### Given Data:
- Initial water level (before rain began): 22 feet
- Water level after 3 days of rain: 34 feet
- Water level after 10 days of rain: 62 feet

### Step 1: Rate of Change
The rate of change can be calculated by the change in water level divided by the change in days.

1. **Calculate change in water level**:
\[
\text{Change after 10 days} = 62 - 22 = 40 \text{ feet}
\]
\[
\text{Change after 3 days} = 34 - 22 = 12 \text{ feet}
\]

2. **Calculate the number of days**:
\[
\text{Total change in days} = 10 - 3 = 7 \text{ days}
\]

3. **Average rate of change (for the full 10 days)**:
\[
\text{Rate of Change} = \frac{40 \text{ feet}}{10 \text{ days}} = 4 \text{ feet per day}
\]

### Step 2: y-intercept
In this context, the y-intercept represents the initial water level before the rain began, which is:
\[
y\text{-intercept} = 22 \text{ feet}
\]

### Step 3: Equation in Point-Slope Form
Using the point (3, 34) as a point on our line, with the slope (rate of change) of 4, the point-slope form of the equation is:
\[
y - 34 = 4(x - 3)
\]

### Step 4: Change to Standard Form
To change the point-slope equation to standard form (Ax + By = C), we can manipulate the equation we derived:

1. Start with:
\[
y - 34 = 4(x - 3)
\]

2. Distribute 4:
\[
y - 34 = 4x - 12
\]

3. Rearrange to standard form:
\[
-4x + y = 22
\]
or multiplying through by -1 to avoid negative A:
\[
4x - y = -22
\]

### Summary of Responses:
1. **Rate of Change**: 4 feet per day
2. **y-intercept**: 22 feet
3. **Point-slope form**: \(y - 34 = 4(x - 3)\)
4. **Standard form**: \(4x - y = -22\)

You can now input these responses into their respective areas.