Suppose that the water level of a river is 34 feet after 3 days of rain and 62 feet after 10 days of rain.

Question

Given the two points we know: (3, 34) and (10, 62), what would the point-slope equation look like?

(1 point)
Responses

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

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

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

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

Answer 1

To find the point-slope equation given the two points (3, 34) and (10, 62), we first need to determine the slope of the line connecting the 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, 34) and (10, 62):

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

Now that we have the slope, we can use the point-slope form of the equation:

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

Using one of the points, let's use (3, 34):

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

Now, let's find the matching expression from the provided options:

The point-slope equation derived is:

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

So the correct choice from your options is:

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