Use the image to answer the question.

(4, 8), 2, (3, 6), 1, (2, 4), 6, (1, 2), (0, 0)
Use the similar triangles to determine the slope of the line.
The slope is __

1 answer

To determine the slope of the line using the coordinates given, we can calculate the slope between two points. The slope \( m \) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:

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

Let's take the first two points from your list:

  1. Point 1: (4, 8)
  2. Point 2: (2, 4)

Using the formula:

  • \( x_1 = 4, y_1 = 8 \)
  • \( x_2 = 2, y_2 = 4 \)

Now plug in the values:

\[ m = \frac{4 - 8}{2 - 4} = \frac{-4}{-2} = 2 \]

Now let's check the slope between points (3, 6) and (1, 2):

  • Point 1: (3, 6)
  • Point 2: (1, 2)

Applying the same formula:

  • \( x_1 = 3, y_1 = 6 \)
  • \( x_2 = 1, y_2 = 2 \)

Now plug in:

\[ m = \frac{2 - 6}{1 - 3} = \frac{-4}{-2} = 2 \]

Finally, we can check from another set, (2, 4) and (0, 0):

  • Point 1: (2, 4)
  • Point 2: (0, 0)

Using the same formula:

  • \( x_1 = 2, y_1 = 4 \)
  • \( x_2 = 0, y_2 = 0 \)

Now plug in:

\[ m = \frac{0 - 4}{0 - 2} = \frac{-4}{-2} = 2 \]

In all cases, the slope calculated is the same. Thus, the slope of the line is:

\[ \text{slope} = 2 \]