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

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

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

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

Answer 1

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

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

Substituting in our points (3, 34) as \((x_1, y_1)\) and (10, 62) as \((x_2, y_2)\):

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

Now we can use the point-slope form of a line, which is given by:

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

Using the point (3, 34):

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

Thus, the correct point-slope equation is:

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

So the answer is:

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