(0,0), (1,3), (2,6), (3,9) what is the slope of the line

Answer 1

To determine the slope of the line passing through the points (0,0), (1,3), (2,6), and (3,9), you can use the slope formula. The slope \( m \) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Let's take two points from the given set and apply the formula. For example, we can use the first two points: \((0,0)\) and \((1,3)\).

Using the points (0,0) and (1,3):

\[ x_1 = 0 \]
\[ y_1 = 0 \]
\[ x_2 = 1 \]
\[ y_2 = 3 \]

Substitute these values into the slope formula:

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

So the slope of the line is \( 3 \).

To confirm this, you can check the slope using any other pair of points from the given set. Let's use the points (1,3) and (2,6):

\[ x_1 = 1 \]
\[ y_1 = 3 \]
\[ x_2 = 2 \]
\[ y_2 = 6 \]

Substitute these values into the slope formula:

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

Again, the slope is \( 3 \).

This consistency across different points confirms that the slope of the line is indeed \( 3 \).