Question

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?

(1 point)
Responses

(y - 34) = 4 (x - 10)
(y - 34) = 4 (x - 10)

(y - 34) = 4 (x - 3)
(y - 34) = 4 (x - 3)

(y - 3) = 4 (x - 34)
(y - 3) = 4 (x - 34)

(y - 10) = 4 (x + 62)

Answer 1

To find the point-slope equation using the two points (3, 34) and (10, 62), we first need to calculate the slope (m) of the line between these two points using the formula:

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

Substituting the given points:

\[
m = \frac{62 - 34}{10 - 3} = \frac{28}{7} = 4
\]

Now that we have the slope (m = 4), we can use the point-slope form of the equation, which is:

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

We can use either of the two points, but let’s use the point (3, 34):

\[
y - 34 = 4(x - 3)
\]

Thus, the point-slope equation is:

\[
(y - 34) = 4 (x - 3)
\]

Therefore, the correct response is:

**(y - 34) = 4 (x - 3)**