The image you've uploaded contains a system of linear equations that need to be solved by graphing. Here are the equations provided:

1. $y = -\frac{1}{2}x + 4$
2. $y = \frac{3}{4}x - 1$

You have already plotted the two lines on the graph. The solution to the system is the point where these two lines intersect.

Analyzing the Graph:

• The two lines intersect at the point $(4, 2)$, as you've noted on the graph.
• This point $(4, 2)$ is the solution to the system of equations because it satisfies both equations.

Verification:

Let's verify by substituting $x = 4$ and $y = 2$ into both equations to ensure it satisfies them.

1. First equation: $y = -\frac{1}{2}x + 4$ $2 = -\frac{1}{2}(4) + 4 = -2 + 4 = 2$ This is true.

2. Second equation: $y = \frac{3}{4}x - 1$ $2 = \frac{3}{4}(4) - 1 = 3 - 1 = 2$ This is also true.

Since the point $(4, 2)$ satisfies both equations, it is indeed the correct solution.

Would you like more details or have any other questions?

Related Questions:

1. How do you graph the equation $y = \frac{1}{4}x + 4$?
2. What is the slope-intercept form of a linear equation?
3. How do you determine the point of intersection for two lines algebraically?
4. What are the possible outcomes when solving a system of linear equations by graphing?
5. How can you check if two lines are parallel or perpendicular by looking at their slopes?

Tip:

When graphing lines, always start by plotting the y-intercept and then use the slope to find another point on the line.