Question

(1,3) (2,6) (3,9)

Use similar triangles to determine the slope of the line.

(1 point)

The slope is

Answer 1

To determine the slope of the line using the points (1, 3), (2, 6), and (3, 9), we can use the concept of similar triangles.

The slope \( m \) of a line can be calculated using the formula:

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

Let's choose two points from the given points to calculate the slope. We can use the points (1, 3) and (2, 6).

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

Next, we can also check the slope between the points (2, 6) and (3, 9):

\[
m = \frac{9 - 6}{3 - 2} = \frac{3}{1} = 3
\]

And between the points (1, 3) and (3, 9):

\[
m = \frac{9 - 3}{3 - 1} = \frac{6}{2} = 3
\]

In all cases, the slope is consistently \( 3 \).

Thus, the slope of the line is:

\[
\text{The slope is } 3.
\]