To determine whether the data given is linear, we need to check if there is a constant rate of change between the $X$ and $Y$ values, which is equivalent to checking if the slope between consecutive points is the same.

You have the following pairs of $(X, Y)$ values:

• $(0, 4)$
• $(1, 12)$
• $(2, 20)$
• $(3, 28)$

Step 1: Calculate the slope between consecutive points

The slope $m$ between 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 calculate the slope between each consecutive pair of points:

1. Between $(0, 4)$ and $(1, 12)$:

$m_1 = \frac{12 - 4}{1 - 0} = \frac{8}{1} = 8$

2. Between $(1, 12)$ and $(2, 20)$:

$m_2 = \frac{20 - 12}{2 - 1} = \frac{8}{1} = 8$

3. Between $(2, 20)$ and $(3, 28)$:

$m_3 = \frac{28 - 20}{3 - 2} = \frac{8}{1} = 8$

Step 2: Conclusion

Since the slope is constant ($m = 8$) between all consecutive points, the relationship between $X$ and $Y$ is linear.

Equation of the Line

Now, we can find the equation of the line. Since the slope $m = 8$ and we have a point $(0, 4)$, we can use the slope-intercept form $y = mx + c$, where $c$ is the y-intercept.

Substitute the known values:

$y = 8x + 4$

So, the equation of the line is:

$y = 8x + 4$

Would you like to go over any details or have further questions?

Here are five related questions:

1. How do you find the slope between two points?
2. What are the characteristics of a