To address this question, I'll assume that the line you're referring to is a straight line based on the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Let's work through the steps.

Part (a): Create a table of ordered-pair solutions

If the equation is linear, the table will contain points that lie on the graph of the line. However, the specific equation or graph isn't provided. So let's break down how to fill in the table:

You can complete the table by identifying at least two points on the graph (by looking at where the graph crosses grid lines). For example, if we have the following points from the graph:

1. $(-2, -4)$
2. $(-1, -2)$
3. $(0, 0)$
4. $(1, 2)$
5. $(2, 4)$

These ordered pairs suggest that the relationship between $x$ and $y$ increases in a regular, predictable way.

Thus, a table of ordered-pair solutions based on these points would look like this:

$x$	$y$
-2	-4
-1	-2
0	0
1	2
2	4

Part (b): Find the equation of the line

Notice the pattern in the table: as $x$ increases by 1, $y$ increases by 2. This constant rate of change indicates that the slope $m = 2$.

The line also passes through the origin $(0, 0)$, which means the y-intercept $b = 0$.

Using the slope-intercept form of a line, $y = mx + b$, we can substitute $m = 2$ and $b = 0$ into the equation:

$y = 2x$

Thus, the equation of the line is $y = 2x$.

Summary

• The table of ordered-pair solutions:
  • $(-2, -4), (-1, -2), (0, 0), (1, 2), (2, 4)$
• The equation of the line is $y = 2x$.

Do you want details or have any questions? Here are five questions to extend your understanding:

1. How do you determine the slope of a line from a table of points?
2. What does the y-intercept represent in the equation of a line?
3. If the line had a different slope, how would that affect the ordered pairs?
4. How can you confirm that a point lies on a line given its equation?
5. What is the general form of a linear equation?

Tip: To find the slope between two points, use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.