Question

Question 2
14. 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?(1 point)
Responses

(y−3)=−5(x−45)
open paren y minus 3 close paren is equal to negative 5 times open paren x minus 45 close paren

(y+10)=−5(x−10)
open paren y plus 10 close paren is equal to negative 5 times open paren x minus 10 close paren

(y−45)=−5(x−3)
open paren y minus 45 close paren is equal to negative 5 times open paren x minus 3 close paren

(y−10)=−5(x+10)

Answer 1

To find the point-slope equation of the line that passes through the points (3, 45) and (10, 10), we first need to calculate the slope (m) of the line.

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( (3, 45) \) and \( (10, 10) \):
- \( (x_1, y_1) = (3, 45) \)
- \( (x_2, y_2) = (10, 10) \)

Calculating the slope:

\[
m = \frac{10 - 45}{10 - 3} = \frac{-35}{7} = -5
\]

Now that we have the slope (m = -5), we can use the point-slope form of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

Using the point \( (3, 45) \):

\[
y - 45 = -5(x - 3)
\]

The equation derived is:

\[
y - 45 = -5(x - 3)
\]

From the options provided, the correct point-slope equation is:

**(y−45)=−5(x−3)**

So, the correct response is:
- (y−45)=−5(x−3)