12. Suppose that the water level of a river is 34 feet after 3 days of rain and 62 feet after 10 days of rain.%0D%0A%0D%0AGiven the two points we know: (3, 34) and (10, 62), what would the point-slope equation look like?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A(y - 3) = 4 (x - 34)%0D%0A(y - 3) = 4 (x - 34)%0D%0A%0D%0A(y - 34) = 4 (x - 10)%0D%0A(y - 34) = 4 (x - 10)%0D%0A%0D%0A (y - 10) = 4 (x + 62)%0D%0A (y - 10) = 4 (x + 62)%0D%0A%0D%0A(y - 34) = 4 (x - 3)%0D%0A(y - 34) = 4 (x - 3)
The correct point-slope equation would be:
(y - 34) = 4 (x - 10)
To find the point-slope equation using the two given points (3, 34) and (10, 62), we can use the slope formula, which is:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the two points into the formula:
m = (62 - 34) / (10 - 3)
m = 28 / 7
m = 4
Once we have the slope, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
Using the point (3, 34) as the point (x1, y1):
y - 34 = 4(x - 3)
Therefore, the correct point-slope equation is:
(y - 34) = 4(x - 3)
To find the point-slope equation, we need to use the two given points: (3, 34) and (10, 62).
The point-slope equation is in the form: y - y1 = m(x - x1), where (x1, y1) is one of the given points, and m is the slope of the line.
First, let's find the slope of the line using the two points:
m = (y2 - y1) / (x2 - x1)
m = (62 - 34) / (10 - 3)
m = 28 / 7
m = 4
Now, we can use any of the given points and the slope to write the point-slope equation. Let's use the point (3, 34):
y - 34 = 4(x - 3)
Therefore, the correct answer is:
(y - 34) = 4 (x - 3)