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)

Question

Responses

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

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

(y−3)=−5(x−45)

Answer 1

To determine the correct point-slope equation based on the provided points (3, 45) and (10, 10), we first need to find the slope of the line connecting these two points.

The slope \( m \) can be calculated using the formula:

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

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

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

Now that we have the slope \( m = -5 \), we can use one of the two points in the point-slope form of the line, which is written as:

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

Using the point (3, 45):

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

Thus, the correct point-slope equation is:

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

So, the correct response is:

(y−45)=−5(x−3)