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%0A22(0,34)4x+y=34%0D%0A4%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A34%0D%0Ay=4x+34%0D%0A%0D%0A=%0D%0A4%0D%0A%0D%0A+%0D%0A34%0D%0Ay=4x−22%0D%0A%0D%0A=%0D%0A4%0D%0A%0D%0A−%0D%0A22%0D%0A−4x+y=34%0D%0A−%0D%0A4%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A34%0D%0Ay=28x+34%0D%0A%0D%0A=%0D%0A28%0D%0A%0D%0A+%0D%0A34%0D%0A28y=4x+22%0D%0A%0D%0A=%0D%0A4%0D%0A%0D%0A+%0D%0A22%0D%0A7(0,0)4(0,22)0−4x+y=22%0D%0A−%0D%0A4%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A22%0D%0A(0,4)
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.
d is wrong
Apologies for the mistake. The correct equation in standard form is 4x - y = -34.
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) in this scenario, we can use the formula:
slope = (change in y)/(change in x)
Given that the water level of the river was 22 feet before the rain began (x = 0), and it became 34 feet after 3 days of rain (x = 3), we have:
change in x = 3 - 0 = 3
change in y = 34 - 22 = 12
So, the slope is:
slope = (change in y)/(change in x) = 12/3 = 4
Therefore, the rate of change (slope) for this scenario is 4.
To find the y-intercept for this scenario, we can use the formula y = mx + b, where m is the slope and b is the y-intercept.
We know that the slope is 4 (as calculated above) and the water level of the river was 22 feet before the rain began (when x = 0).
So, we have:
y = 4x + b
22 = 4(0) + b
Simplifying the equation, we get:
b = 22
Therefore, the y-intercept for this scenario is 22.
To write an equation for the scenario in slope-intercept form (y = mx + b), we can use the values we calculated above:
slope (m) = 4
y-intercept (b) = 22
So, the equation in slope-intercept form is:
y = 4x + 22
To write this equation in standard form (Ax + By = C), we need to rearrange the equation:
y = 4x + 22
Subtracting 4x from both sides, we get:
-4x + y = 22
So, the equation in standard form is:
-4x + y = 22