The graph shows two linear equations:

1. $y = x - 3$: This line has a slope of 1 and a y-intercept of -3.
2. $y = 2x - 4$: This line has a slope of 2 and a y-intercept of -4.

Sketching the two lines:

1. For $y = x - 3$:

   • The y-intercept is -3 ($(0, -3)$).
   • With a slope of 1, for every 1 unit increase in $x$, $y$ increases by 1.
   • Plot another point at $(1, -2)$, and so on.

2. For $y = 2x - 4$:

   • The y-intercept is -4 ($(0, -4)$).
   • With a slope of 2, for every 1 unit increase in $x$, $y$ increases by 2.
   • Plot another point at $(1, -2)$, and so on.

The graph already shows these two lines correctly plotted.

Let me know if you'd like a breakdown of specific points, the intersection of the two lines, or more details on graphing linear equations.

Questions for deeper understanding:

1. How do you calculate the intersection point of the two lines algebraically?
2. What does the slope of a line tell you about its steepness or direction?
3. What are the implications of parallel or perpendicular slopes in two lines?
4. How do you determine whether two lines intersect or are parallel using their equations?
5. How would the graph change if you altered the slopes or y-intercepts of these equations?

Tip: Always start plotting a line by identifying the y-intercept and using the slope to determine additional points.