To find the equations for the two parallel lines shown in the graph, we can follow these steps:

Step 1: Identify the Slope

Since the lines are parallel, they share the same slope. Looking at the lines, we can determine the slope by identifying two points on one of the lines and using the formula:

$\text{slope} = \frac{{\Delta y}}{{\Delta x}}$

Let’s use the top line, which passes through the points:

• $(0, 6)$
• $(4, 8)$

Using these points: $\text{slope} = \frac{8 - 6}{4 - 0} = \frac{2}{4} = \frac{1}{2}$

Step 2: Find the Equation for the Top Line

The top line crosses the y-axis at $y = 6$. Thus, its equation is:

$y = \frac{1}{2}x + 6$

Step 3: Find the Equation for the Bottom Line

The bottom line is parallel to the top line, so it also has a slope of $\frac{1}{2}$. Observing the y-intercept of the bottom line, we see it crosses the y-axis at $y = -6$. Therefore, the equation for the bottom line is:

$y = \frac{1}{2}x - 6$

Final Answer:

• Equation for the top line: $y = \frac{1}{2}x + 6$
• Equation for the bottom line: $y = \frac{1}{2}x - 6$

Would you like further details on any of these steps, or do you have any questions?

Additional Questions:

1. How do you determine if two lines are parallel or perpendicular based on their slopes?
2. What changes in the equations if the lines were perpendicular instead of parallel?
3. How do you find the equation of a line if you are given a point and the slope?
4. What is the significance of the y-intercept in the equation of a line?
5. How can you graph a line if only given its equation in slope-intercept form?

Tip:

Remember, for parallel lines, the slopes are always identical, but the y-intercepts are different.