Suppose that the water level of a river is 34 feet after 3 days of rain and 62 feet after 10 days of rain.
Given the two points we know: (3, 34) and (10, 62), what would the point-slope equation look like?
y - 3) = 4 (x - 34)
(y - 34) = 4 (x - 10)
(y - 10) = 4 (x + 62)
(y - 34) = 4 (x - 3)
(y - 34) = 4 (x - 3)
The correct point-slope equation for the given points is:
(y - 34) = 4 (x - 3)
To find the point-slope equation given two points, we can use the formula:
(y - y1) = m (x - x1)
Where (x1, y1) represents one of the given points and m represents the slope of the line.
Using the points (3, 34) and (10, 62), we can find the slope m using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given values:
m = (62 - 34) / (10 - 3)
m = 28 / 7
m = 4
Now we can choose one of the given points, let's say (3, 34), and substitute its coordinates into the point-slope equation:
(y - 34) = 4 (x - 3)
So, the correct point-slope equation for the given points is:
(y - 34) = 4 (x - 3)