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?
A. (y - 34) = 4(x - 3)
B. (y - 34) = (x - 10)
C. (y - 10) = 4(x + 62)
D. (y - 3) = 4(x - 34)

Answer 1

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

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

Using the points (3, 34) and (10, 62):

• \( (x_1, y_1) = (3, 34) \)
• \( (x_2, y_2) = (10, 62) \)

Now, substituting the coordinates into the slope formula:

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

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

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

We can choose either point to write the equation. Let's use the point (3, 34):

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

This matches option A:

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

So the correct answer is A.