Question

Solve the following system of equations graphically on the set of axes below.
y, equals, minus, one half, x, plus, 4
y=−
2
1
​
x+4
y, equals, 2, x, minus, 1
y=2x−1
Plot two lines by clicking the graph.
Click a line to delete it.
give very detailed instructions on how to graph this

Answer 1

To graph the system of equations given, you will need to plot both lines on the same set of axes. Here are detailed instructions on how to do this:

### Equations to Graph
1. **Equation 1**: \( y = -\frac{1}{2}x + 4 \)
2. **Equation 2**: \( y = 2x - 1 \)

### Steps to Graph the Equations

#### Step 1: Graph the First Equation \( y = -\frac{1}{2}x + 4 \)
1. **Identify the y-intercept**: The y-intercept of this line is \( 4 \) (the point where the line crosses the y-axis). Plot the point \( (0, 4) \) on the graph.
2. **Identify the slope**: The slope of the line is \( -\frac{1}{2} \). This means for every 1 unit you move to the right (positive direction on x-axis), the line will go down by \( \frac{1}{2} \) units (negative direction on y-axis).
3. **Plot another point**: From the point \( (0, 4) \), move 2 units to the right to \( (2, 4) \). From there, move down 1 unit to \( (2, 3) \). Plot the point \( (2, 3) \).
4. **Draw the line**: Connect the two points \( (0, 4) \) and \( (2, 3) \) with a straight line. Extend the line to the edges of the graph.

#### Step 2: Graph the Second Equation \( y = 2x - 1 \)
1. **Identify the y-intercept**: The y-intercept of this line is \( -1 \). Plot the point \( (0, -1) \) on the graph.
2. **Identify the slope**: The slope is \( 2 \). This means for every 1 unit you move to the right, the line will go up by 2 units.
3. **Plot another point**: From the y-intercept \( (0, -1) \), move 1 unit to the right to \( (1, -1) \). From there, move up 2 units to \( (1, 1) \). Plot the point \( (1, 1) \).
4. **Draw the line**: Connect the two points \( (0, -1) \) and \( (1, 1) \) with a straight line. Extend this line to the edges of the graph.

### Step 3: Find the Intersection Point
After graphing both lines, look for the point where they intersect. This intersection point represents the solution to the system of equations.

### Step 4: Label Your Graph
1. Label the first line \( y = -\frac{1}{2}x + 4 \).
2. Label the second line \( y = 2x - 1 \).
3. If you identified the intersection point, label it with coordinates (e.g., \( (x, y) \)).

### Conclusion
Now your graph should display two lines, and where they intersect is the solution to the system. If you’re using graphing software or a graphing calculator, enter the equations as they are. If you are drawing by hand, follow the points described above carefully for accuracy.