To determine the equation of the linear relationship represented in the table, we can first calculate the slope (m) using the points provided.
We have the following points from the table:
- (0, -6)
- (1, -3)
- (2, 0)
- (3, 3)
To find the slope (m), we can use the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (0, -6) and (1, -3):
\[ m = \frac{-3 - (-6)}{1 - 0} = \frac{-3 + 6}{1} = \frac{3}{1} = 3 \]
Now that we have the slope (m = 3), we can use point-slope form to find the equation of the line. We can use one of the points, for example, (0, -6). The equation in point-slope form is:
\[ y - y_1 = m(x - x_1) \]
Substituting \(m\) and the point (0, -6):
\[ y - (-6) = 3(x - 0) \]
This simplifies to:
\[ y + 6 = 3x \]
Subtracting 6 from both sides gives us:
\[ y = 3x - 6 \]
In slope-intercept form (y = mx + b), the equation is:
\[ y = 3x - 6 \]
Thus, the correct equation of the linear relationship is:
\[ \boxed{y = 3x - 6} \]