Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no rain. The river was 60 feet before the drought began.(4 points) 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. 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 an equation in standard form.
a. The rate of change (slope) for this scenario can be calculated using the formula:
slope = (change in y)/(change in x)
Let's calculate the change in y and change in x first:
- Change in y = 45 - 10 = 35 feet
- Change in x = 3 - 10 = -7 days (as the number of days without rain is decreasing)
Now, we can calculate the slope:
slope = (35 feet)/(-7 days) = -5 feet/day
b. The y-intercept for this scenario is the water level at the beginning of the drought, which is 60 feet.
c. To write the equation in slope-intercept form, we can use the formula:
y = mx + b
where m is the slope and b is the y-intercept.
So the equation can be written as:
y = -5x + 60
d. To write the equation in standard form, we can rearrange the equation in slope-intercept form:
y = -5x + 60
Rearranging, we get:
5x + y = 60
So the equation in standard form is:
5x + y - 60 = 0
the last one is not an option
Apologies for the confusion. The equation in standard form is not available as an option for this scenario.
the options are y + -5x + 60
15
y = -5x - 35
(-5, 0)
y = 5x + 45
5x + y = 35
5
(0, -5)
-5 + y = 60
5x + y = 60
-5
(0, 60)
In that case, the correct responses for each question would be:
a. The rate of change (slope) for this scenario is 5.
b. The y-intercept for this scenario is 60.
c. The equation for the scenario in slope-intercept form is y = 5x + 60.
d. The equation in standard form is 5x + y = 60.
c is not one of the options
Apologies for the mistake.
The correct equation in slope-intercept form for this scenario is y = -5x + 60.
so b is (0, 60) ?
Yes, that is correct. The y-intercept for this scenario is (0, 60).
a. 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 the difference in water level, which is 60 feet - 10 feet = 50 feet. The change in x is the number of days, which is 10 days - 3 days = 7 days.
So the slope is 50 feet / 7 days = 7.14 feet per day.
b. The y-intercept is the value of y when x is 0. In this scenario, when there are no days of no rain, the water level is 60 feet. So the y-intercept is 60 feet.
c. To write the equation for the scenario in slope-intercept form (y = mx + b), we can plug in the values we have:
y = 7.14x + 60
d. To write the equation in standard form (Ax + By = C), we can rearrange the equation from slope-intercept form:
-7.14x + y = 60
Multiplying through by 100 to eliminate decimals:
-714x + 100y = 6000