Question

The table shown represents a linear relationship.

x 0 1 2 3
y −6 −3 0 3


Based on the table, what is the equation of the linear relationship in slope-intercept form?
y = −3x + 2
y = −3x − 2
y = 3x + 6
y = 3x − 6

Answer 1

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:

\[
\boxed{y = 3x - 6}
\]