suppose that the water level of a river is 34 feet after 3 days of rain and 62 feet after 10 days or rain. the river was 22 feet before the rain began.
A.what is the rate of change (slope) for this scenario? ______
B. what is the y-intercept for this scenario?_______
C. write an equation for this scenario in slope-intercept from____
D. write this equation in standard form.____
1. y = 4x + 34
2. (0,22)
3.-4x + y = 34
4.7
5.-4x + y = 22
6. y = 4x +22
7.4
8. 4x + y = 34
9. (0,0)
10. y = 28x + 34
11. (0,34)
12. (0,4)
13. y = 4x - 22
14. 28
15. 22
26.0
A. The rate of change (slope) for this scenario can be found by calculating the change in y-coordinates (water level) divided by the change in x-coordinates (days of rain).
Rate of change = (62 - 34) / (10 - 3) = 28/7 = 4
B. The y-intercept for this scenario is the initial water level before the rain began, which is 22 feet.
C. The equation for this scenario in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Therefore, the equation is y = 4x + 22.
D. To write this equation in standard form, it needs to be rearranged so that the x and y terms are on the same side of the equation and the coefficient of x is positive.
So, -4x + y = 22 is the equation in standard form.
are you sure
I apologize for any mistakes in my previous response. Let's go through the questions again:
A. The rate of change (slope) for this scenario can be found by calculating the change in y-coordinates (water level) divided by the change in x-coordinates (days of rain).
Rate of change = (62 - 34) / (10 - 3) = 28/7 = 4
B. The y-intercept for this scenario is the initial water level before the rain began, which is 22 feet.
C. The equation for this scenario in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Therefore, the equation is y = 4x + 22.
D. To write this equation in standard form, it needs to be rearranged so that the x and y terms are on the same side of the equation and the coefficient of x is positive.
So, the equation in standard form is 4x - y = -22.
Based on this information, the correct answers would be:
A. 4
B. 22
C. y = 4x + 22
D. 4x - y = -22
To solve the given scenario step-by-step:
Step 1: Identifying the data given
- The water level of the river is 34 feet after 3 days of rain.
- The water level of the river is 62 feet after 10 days of rain.
- The river was initially at 22 feet before the rain began.
Step 2: Calculating the rate of change (slope)
- The rate of change (slope) can be calculated by finding the difference in water level over the difference in time.
- Slope = (Change in y / Change in x) = (62 - 34) / (10 - 3)
- Slope = 28 / 7 = 4
So, the rate of change (slope) for this scenario is 4.
Step 3: Finding the y-intercept
- The y-intercept is the value of y when x (time) is 0.
- In this scenario, the water level of the river was 22 feet before the rain began.
- Therefore, the y-intercept is 22.
So, the y-intercept for this scenario is 22.
Step 4: Writing the equation in slope-intercept form
- The slope-intercept form of the equation is y = mx + b, where m is the slope and b is the y-intercept.
- Substituting the values, we get the equation: y = 4x + 22.
So, the equation for this scenario in slope-intercept form is y = 4x + 22.
Step 5: Writing the equation in standard form
- Standard form of the equation is Ax + By = C, where A, B, and C are constants.
- Rearranging the equation y = 4x + 22, we get -4x + y = 22.
So, the equation for this scenario in standard form is -4x + y = 22.
To summarize the answers:
A. The rate of change (slope) for this scenario is 4.
B. The y-intercept for this scenario is 22.
C. The equation for this scenario in slope-intercept form is y = 4x + 22.
D. The equation for this scenario in standard form is -4x + y = 22.
To find the answers to these questions, we need to analyze the information given and use it to write an equation representing the relationship between the number of days of rain (x) and the water level of the river (y).
Step 1: Determine the rate of change (slope)
The rate of change represents how much the water level of the river changes for each additional day of rain. To find it, we can calculate the difference in water level (y) and the difference in the number of days of rain (x) between two given points.
Given:
- After 3 days of rain: water level = 34 feet
- After 10 days of rain: water level = 62 feet
Difference in y (water level): 62 - 34 = 28
Difference in x (number of days): 10 - 3 = 7
Rate of change (slope) = difference in y / difference in x = 28 / 7 = 4
So, the rate of change (slope) for this scenario is 4.
Option: 7. 4 (the correct answer)
Step 2: Determine the y-intercept
The y-intercept represents the water level of the river when it started raining (before any days of rain). In this case, the water level was 22 feet.
So, the y-intercept for this scenario is 22.
Option: 15. 22 (the correct answer)
Step 3: Write an equation in slope-intercept form (y = mx + b)
Now that we know the slope (4) and the y-intercept (22), we can write the equation in slope-intercept form:
y = 4x + 22
Option: 6. y = 4x + 22 (the correct answer)
Step 4: Write the equation in standard form (Ax + By = C)
To convert the equation from slope-intercept form to standard form, we need to rearrange it so that the x and y terms are on one side and the constant term is on the other side.
Start with the equation in slope-intercept form:
y = 4x + 22
Multiply through by -1 to change the sign of all terms:
-y = -4x - 22
Rearrange the equation by moving all terms to one side:
4x + y = 22
So, the equation in standard form is:
4x + y = 22
Option: 8. 4x + y = 22 (the correct answer)
To summarize the correct answers:
A. The rate of change (slope) for this scenario is 4. (Option 7)
B. The y-intercept for this scenario is 22. (Option 15)
C. The equation for this scenario in slope-intercept form is y = 4x + 22. (Option 6)
D. The equation for this scenario in standard form is 4x + y = 22. (Option 8)