Use similar triangles to determine the slope of the line. Write your answer in fraction form. the numbers are (8,4), (6,3) (4,2) (2,1) and (0,0) The slope is __

1 answer

To determine the slope of the line using the points provided, we first need to choose two points. The slope \( m \) is calculated using the formula:

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

Let's select the points (0, 0) and (8, 4).

Here:

  • \( (x_1, y_1) = (0, 0) \)
  • \( (x_2, y_2) = (8, 4) \)

Now, substituting these values into the slope formula:

\[ m = \frac{4 - 0}{8 - 0} = \frac{4}{8} = \frac{1}{2} \]

We can verify this by using any other pair of points from the list. Let's check using the points (2, 1) and (8, 4):

Here:

  • \( (x_1, y_1) = (2, 1) \)
  • \( (x_2, y_2) = (8, 4) \)

Now substituting these values into the slope formula:

\[ m = \frac{4 - 1}{8 - 2} = \frac{3}{6} = \frac{1}{2} \]

If we choose another pair (6, 3) and (0, 0):

\[ m = \frac{3 - 0}{6 - 0} = \frac{3}{6} = \frac{1}{2} \]

All pairs yield a consistent slope. Hence, the slope of the line is:

\[ \text{slope} = \frac{1}{2} \]