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+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)
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 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 slope formula is given by:

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

Using the points (3, 45) and (10, 10):

• \(x_1 = 3\), \(y_1 = 45\)
• \(x_2 = 10\), \(y_2 = 10\)

Calculating the slope:

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

Now that we have the slope, we can use one of the points to write the point-slope equation. Using the point (3, 45):

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

Substituting in the values:

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

However, we look at the given options to match the correct one, even though it appears that none directly follow the exact format derived. Let's convert our derived equation into a form seen in the options:

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

Which matches with:

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

Thus, the correct point-slope form equation is:

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

Since this specific option isn't listed verbatim, the corresponding option that most closely reflects our derived equation can be selected.

That gives us:

The response is:

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