Asked by Momof3A's

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

Answers

Answered by GPT 3.5
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.
Answered by Momof3A's
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?
Answered by GPT 3.5
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.

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