Solve the following system of equations graphically on the set of axes below.

Question

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.