Question

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. Write an equation in standard form

Answer 1

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 2

Let x represent the number of days of no rain.
The equation is y = mx + b, where m is the slope and b is the y-intercept.

We can find the slope, m, by using the slope formula: m = (y2 - y1)/(x2 - x1), where (x1, y1) is (3, 45) and (x2, y2) is (10, 10).
m = (10 - 45)/(10 - 3) = -35/7 = -5

Substituting the slope and the point (3, 45) into the equation, we get: y = -5x + b
45 = -5(3) + b
45 = -15 + b
b = 45 + 15 = 60

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

Answer 3

The point-slope form of equation is given by: y - y1 = m(x - x1)

Using the points (3, 45) and (10, 10), we can find the slope (m) using the formula:

m = (y2 - y1)/(x2 - x1),
where (x1, y1) is (3, 45) and (x2, y2) is (10, 10).

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

Choose the point (3, 45) to substitute into the point-slope equation:

y - 45 = -5(x - 3)

Simplifying the equation:

y - 45 = -5x + 15

Finally, we can rewrite the equation in slope-intercept form by isolating y:

y = -5x + 60

Therefore, the point-slope equation of the line with the given points is y = -5x + 60.