Solve the following system of equations graphically on the set of axes below.
y=-1/2x+8
y=x+2
Plot two lines by clicking the graph.

To solve the system of equations graphically, we'll plot the two lines and identify the intersection point, which will be the solution to the system.

The two equations are:
1. \( y = -\frac{1}{2}x + 8 \)
2. \( y = x + 2 \)

Let's go step by step:

### 1. Equation: \( y = -\frac{1}{2}x + 8 \)
This is a straight line in slope-intercept form \( y = mx + b \), where the slope \( m = -\frac{1}{2} \) and the y-intercept \( b = 8 \).
- **Y-intercept:** The line crosses the y-axis at (0, 8).
- **Slope:** The slope tells us that for every 2 units you move horizontally to the right, the line moves 1 unit down.

### 2. Equation: \( y = x + 2 \)
This is also a line in slope-intercept form, where the slope \( m = 1 \) and the y-intercept \( b = 2 \).
- **Y-intercept:** The line crosses the y-axis at (0, 2).
- **Slope:** The slope tells us that for every 1 unit you move horizontally to the right, the line moves 1 unit up.

### Steps to Graph:
- **Plot the y-intercepts** of both lines: (0, 8) for the first line, and (0, 2) for the second.
- **Apply the slope** from the y-intercept to plot additional points for each line. For the first line, use a slope of -1/2; for the second line, use a slope of 1.

Once the lines are plotted, the point where they intersect is the solution to the system.

I don't have an interactive graphing tool here, but you can graph the two lines following these steps, and the intersection point will give you the solution. If you want a specific graph, you can also upload a set of axes or I can further help you to sketch one.

Would you like me to provide more detailed steps on graphing or help you plot it another way? Let me know if you have any questions.

Here are 5 related questions for further practice:
1. What is the solution to the system if the lines were parallel?
2. How can you check your graphically-found solution algebraically?
3. How would you graph a line if it was given in standard form, like \( 2x + 3y = 6 \)?
4. What is the meaning of the slope of a line?
5. How would the graph change if the y-intercept of the second equation was changed to 4?

**Tip:** Always double-check the slope when plotting points to ensure accuracy on the graph.

Solve the following system of equations graphically on the set of axes below. y=-1/2x+8, y=x+2. Plot two lines by clicking the graph.

Learn how to solve the system of linear equations y = -1/2x + 8 and y = x + 2 graphically. This guide covers key concepts like graphing lines using slope and intercept, identifying the point of intersection, and understanding the solution to a system of equations. Ideal for students in Grades 8-10.

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