To find the slope of the line using the given points, we can use the formula for slope, which is defined as the change in \( y \) divided by the change in \( x \):
\[ \text{slope} (m) = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
We can use any two points from the given (0,0), (1,4), (2,8), (3,12).
Let's take the first two points: (0,0) and (1,4).
Using these points:
- \( x_1 = 0 \), \( y_1 = 0 \)
- \( x_2 = 1 \), \( y_2 = 4 \)
Now, substituting these values into the slope formula:
\[ m = \frac{4 - 0}{1 - 0} = \frac{4}{1} = 4 \]
So the slope of the line is \( 4 \).
We can verify this with another pair of points, such as (1,4) and (2,8):
- \( x_1 = 1 \), \( y_1 = 4 \)
- \( x_2 = 2 \), \( y_2 = 8 \)
Substituting again:
\[ m = \frac{8 - 4}{2 - 1} = \frac{4}{1} = 4 \]
Finally, using the last two points (2,8) and (3,12):
- \( x_1 = 2 \), \( y_1 = 8 \)
- \( x_2 = 3 \), \( y_2 = 12 \)
Substituting again:
\[ m = \frac{12 - 8}{3 - 2} = \frac{4}{1} = 4 \]
In all cases, we end up with a slope of \( 4 \). Therefore, the slope of the line is \( 4 \).