From the image provided, we are asked to determine the coordinates of points A and B. Let's break down the information and tackle the problem step by step.

Key Information:

• We have three lines: $g1$, $g2$, and $g3$.
• $g2$ is given as $y = x + 2$.
• It is stated that $g2$ and $g3$ are parallel.
• The graph provides values along the axes, with the points A and B indicated.

Steps to Solve:

1. Parallelism of $g2$ and $g3$: Since $g2$ and $g3$ are parallel, $g3$ will have the same slope as $g2$. Therefore, $g3$ will also have the form $y = x + c$, where $c$ is a constant to be determined.

2. Finding Point A: Point A lies on both $g2$ and $g3$. Since $g2$ is given by the equation $y = x + 2$, we can substitute the value of $x$ and $y$ from the graph. For $A$, it appears that $x = 5$ and $y = 7$. Substituting into $g2$: $y = 5 + 2 = 7$ Thus, point A is located at $(5, 7)$.

3. Finding Point B: Point B lies on line $g1$. From the graph, $g1$ appears to be a horizontal line passing through $y = 8$. Therefore, the y-coordinate of point B is 8, and the x-coordinate is where this line intersects $g2$. We solve for $x$ by setting $y = 8$ in the equation $y = x + 2$: $8 = x + 2 \quad \Rightarrow \quad x = 6$ Hence, point B is located at $(6, 8)$.

Summary of Coordinates:

• Point A: $(5, 7)$
• Point B: $(6, 8)$

Would you like more details or explanations on any part of this solution?

Related Questions:

1. How can you determine the equation of a line if two points are given?
2. What is the general formula for finding the intersection of two lines?
3. How do you check if two lines are parallel?
4. How can you calculate the distance between two points on a graph?
5. What are the properties of parallel lines in terms of their slopes?

Tip:

Remember, parallel lines always have the same slope, which makes their equations differ only by their y-intercept!