13. 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)

Question

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 the scenario in slope-intercept form, _______. Write an equation in standard form

Answer 1

a. The rate of change (slope) for this scenario can be calculated by finding the difference in water level divided by the difference in time.

Change in water level = 60 ft - 10 ft = 50 ft
Change in time = 10 days - 3 days = 7 days

Rate of change = change in water level / change in time
Rate of change = 50 ft / 7 days ≈ 7.14 ft/day

b. The y-intercept represents the initial water level before the drought began. In this scenario, the y-intercept is 60 ft.

c. To write the equation in slope-intercept form, we use the y-intercept and the rate of change:
y = mx + b
where m is the slope and b is the y-intercept.

Using the given values:
y = 7.14x + 60

To write the equation in standard form, we rearrange the equation:
-7.14x + y = 60

So the equation in slope-intercept form is y = 7.14x + 60, and the equation in standard form is -7.14x + y = 60.

Answer 2

13. 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)
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 the scenario in slope-intercept form, _______.
d. Write an equation in standard form. _______

Answer 3

a. The rate of change (slope) for this scenario can be calculated by finding the difference in water level divided by the difference in time.

Change in water level = 60 ft - 10 ft = 50 ft
Change in time = 10 days - 3 days = 7 days

Rate of change = change in water level / change in time
Rate of change = 50 ft / 7 days ≈ 7.14 ft/day

b. The y-intercept represents the initial water level before the drought began. In this scenario, the y-intercept is 60 ft.

c. To write the equation in slope-intercept form, we use the y-intercept and the rate of change:
y = mx + b
where m is the slope and b is the y-intercept.

Using the given values:
y = 7.14x + 60

d. To write the equation in standard form, we rearrange the equation:
-7.14x + y = 60

Answer 4

14. 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. Given the two points we know: (3, 45) and (10, 10), what would the point slope equation look like?(1 point

Answer 5

The point-slope equation can be written as:

y - y1 = m(x - x1)

where (x1, y1) is one of the given points and m is the slope.

Using the two points (3, 45) and (10, 10), let's first calculate the slope:

Slope (m) = (change in y) / (change in x)
= (10 - 45) / (10 - 3)
= -35 / 7
= -5

Now let's choose one of the points, say (3, 45), and plug it into the equation:

y - y1 = m(x - x1)
y - 45 = -5(x - 3)

So the point-slope equation, using the point (3, 45), would look like:

y - 45 = -5(x - 3)