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? 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.

Answer 1

To find the rate of change (slope), we can use the formula:

slope = change in y / change in x

In this scenario, the change in y is the difference in the water level, which is 45 feet - 10 feet = 35 feet. The change in x is the difference in the number of days, which is 10 days - 3 days = 7 days.

So the slope is 35 feet / 7 days = 5 feet/day.

b. The y-intercept is the value of y when x is 0. In this scenario, at the beginning of the drought, the water level was 60 feet. Therefore, the y-intercept is 60.

c. To write the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we have:

y = 5x + 60

d. The standard form of an equation is written as Ax + By = C, where A, B, and C are constants. We can rearrange the slope-intercept form equation to standard form by moving all terms to one side:

-5x + y = 60

Multiplying through by -1 to make the coefficient of x positive:

5x - y = -60

Therefore, the equation in standard form is 5x - y = -60.

Answer 2

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?

Answer 3

To find the point-slope equation using the two given points (3, 45) and (10, 10), we can use the formula:

y - y1 = m(x - x1)

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

First, let's find the slope using the formula:

m = (y2 - y1) / (x2 - x1)

Using the points (3, 45) and (10, 10):

m = (10 - 45) / (10 - 3)
m = -35 / 7
m = -5

Now, substituting the values of (x1, y1) = (3, 45) and m = -5 into the point-slope equation:

y - 45 = -5(x - 3)

Simplifying and distributing -5:
y - 45 = -5x + 15

Finally, let's rearrange the equation into slope-intercept form:
y = -5x + 60

So, the point-slope equation for the given points is y - 45 = -5(x - 3).