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

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

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

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

Answer 1

To find the point-slope equation for the line that passes through the points (3, 34) and (10, 62), we first need to determine the slope (m) of the line using the formula:

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

Let's identify the coordinates:
- \( (x_1, y_1) = (3, 34) \)
- \( (x_2, y_2) = (10, 62) \)

Calculating the slope:

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

Now we can use the point-slope form of the equation, which is:

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

Using the point \( (3, 34) \):

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

So, the point-slope equation is:

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

Comparing this to the provided options, the correct choice is:

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