The problem is asking for the equation of a line that is parallel to the given line and passes through the point (-2, -4).

Step 1: Find the slope of the given line

To write the equation of a parallel line, we need to find the slope of the given line. From the graph, we can determine two points on the line, for example:

• (0, 0)
• (2, 2)

Using the slope formula, $m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$: $m = \frac{{2 - 0}}{{2 - 0}} = \frac{2}{2} = 1$ So, the slope $m = 1$.

Step 2: Use point-slope form

Now that we know the slope of the parallel line is also $m = 1$, we use the point-slope form of a line, which is: $y - y_1 = m(x - x_1)$ We substitute the point (-2, -4) and the slope $m = 1$: $y - (-4) = 1(x - (-2))$ Simplifying: $y + 4 = 1(x + 2)$ $y + 4 = x + 2$ $y = x + 2 - 4$ $y = x - 2$

Final Answer:

The equation of the line that is parallel to the given line and passes through the point (-2, -4) is: $y = x - 2$

Would you like further details or have any questions? Here are five related questions for more practice:

1. How would the equation change if the point given was (1, 3)?
2. What is the equation of a line perpendicular to the given line passing through (-2, -4)?
3. How do you determine if two lines are parallel using their slopes?
4. Can a line passing through (-2, -4) ever intersect the given line? Why or why not?
5. How can you graph a line given its equation in slope-intercept form?

Tip: To identify parallel lines, always check that their slopes are the same.