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)
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a. What is the rate of change (slope) for this scenario? Response area
b. What is the y-intercept for this scenario? Response area
c. Write an equation for the scenario in slope-intercept form. Response area
d. Write this equation in standard form. Response Area
Responses
-4x+y=22, y=28x+34, y=4x+34, 22, 0, 4x+y=34, (0,4), 4, y=4x-22, y=4x+22, (0,0), (0,22), 28, 7, -4x+y=34, (0,34)
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.
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 feet, and the change in x is 10 - 3 = 7 days. So, the slope is 28/7 = 4.
To find the y-intercept for this scenario, we need to determine the value of y when x (number of days) is 0. From the information given, we know that before the rain began, the water level was 22 feet. Therefore, the y-intercept is 22.
The equation for the scenario in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Substituting the values we found, the equation becomes y = 4x + 22.
To write this equation in standard form, we need to move the x term to the left side of the equation. The standard form is Ax + By = C. Rearranging the equation y = 4x + 22, we get -4x + y = 22.
Therefore:
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.