11. 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)%0D%0APut 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.%0D%0Aa. What is the rate of change (slope) for this scenario? Response area%0D%0A%0D%0Ab. What is the y-intercept for this scenario? Response area %0D%0A%0D%0Ac. Write an equation for the scenario in slope-intercept form. Response area%0D%0A%0D%0Ad. Write this equation in standard form. Response area%0D%0A%0D%0Ay=28x+34%0D%0A%0D%0A=%0D%0A28%0D%0A%0D%0A+%0D%0A34%0D%0A4x+y=34%0D%0A4%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A34%0D%0A0−4x+y=22%0D%0A−%0D%0A4%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A22%0D%0A22−4x+y=34%0D%0A−%0D%0A4%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A34%0D%0A(0,22)7(0,34)(0,0)y=4x+34%0D%0A%0D%0A=%0D%0A4%0D%0A%0D%0A+%0D%0A34%0D%0A4y=4x−22%0D%0A%0D%0A=%0D%0A4%0D%0A%0D%0A−%0D%0A22%0D%0Ay=4x+22%0D%0A%0D%0A=%0D%0A4%0D%0A%0D%0A+%0D%0A22%0D%0A(0,4)28%0D%0AQuestion
a. What is the rate of change (slope) for this scenario?
The rate of change (slope) for this scenario is 4.
b. What is the y-intercept for this scenario?
The y-intercept for this scenario is 34.
c. Write an equation for the scenario in slope-intercept form.
The equation for the scenario in slope-intercept form is y = 4x + 34.
d. Write this equation in standard form.
The equation in standard form is 4x - y = -34.
Let's solve this step-by-step:
a. To find the rate of change (slope), we can use the formula:
slope = (y2 - y1) / (x2 - x1)
Using the given data, we can use the points (3, 34) and (10, 62):
slope = (62 - 34) / (10 - 3)
= 28 / 7
= 4
Therefore, the rate of change (slope) for this scenario is 4.
b. The y-intercept is the value of y when x is 0. Since the river was 22 feet before the rain began, the y-intercept is 22.
c. Now let's write the equation for the scenario in slope-intercept form, which is:
y = mx + b
Where:
m = slope = 4
b = y-intercept = 22
Therefore, the equation is:
y = 4x + 22.
d. Finally, let's write this equation in standard form, which is:
Ax + By = C
Rearranging the equation from slope-intercept form, we have:
y = 4x + 22
Subtracting 4x from both sides:
-4x + y = 22
Multiplying the equation by -1 to ensure that A is positive:
4x - y = -22
Therefore, the equation in standard form is:
4x - y = -22.
So, the correct answers are:
a. The rate of change (slope) for this scenario is 4.
b. The y-intercept for this scenario is 22.
c. The equation for the scenario in slope-intercept form is y = 4x + 22.
d. The equation in standard form is 4x - y = -22.
To find the rate of change (slope) for this scenario, we can use the formula:
slope = (change in y) / (change in x)
In this case, the change in y is 62 - 34 = 28 (the water level increased by 28 feet), and the change in x is 10 - 3 = 7 (the number of days rain occurred).
So, the slope is:
slope = 28 / 7 = 4
Therefore, the rate of change (slope) for this scenario is 4.
To find the y-intercept, we can use the slope-intercept form of the equation:
y = mx + b
where m is the slope and b is the y-intercept.
In this case, we already know the slope is 4. We can use one of the given points (22 feet before the rain began) to find the y-intercept.
Using the point (0, 22), we have:
22 = 4(0) + b
b = 22
Therefore, the y-intercept for this scenario is 22.
Now, we can write the equation for the scenario in slope-intercept form:
y = 4x + 22
To write this equation in standard form, we move the variables to one side and the constant term to the other side:
-4x + y = 22
Hence, the equation in standard form is 4x - y = -22.