To graph the system of equations, we'll proceed by plotting each equation on the same coordinate grid.
**Step 1: Graphing the first equation, y = -3x + 8**
This is a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.
- The slope (m) for this line is -3, which means the line will fall 3 units on the y-axis for every 1 unit it moves to the right on the x-axis (or rise 3 units if it moves to the left).
- The y-intercept (b) is 8, which is the point on the y-axis where the line crosses it. This gives us our starting point, (0, 8).
To graph this line:
- Start by marking the y-intercept at (0, 8) on the y-axis.
- From there, use the slope to find the next point. Go one unit to the right (x = 1), and then down 3 units (y = 8 - 3 = 5) and put a second point at (1, 5).
- Alternatively, start from the y-intercept and go one unit to the left (x = -1) and up 3 units (y = 8 + 3 = 11), and put a point at (-1, 11).
- Connect these points with a straight line.
**Step 2: Graphing the second equation, y = -2x + 4**
This equation also has the form y = mx + b, with:
- The slope (m) being -2. The line will fall 2 units on the y-axis for each unit to the right on the x-axis.
- The y-intercept (b) is 4, so our starting point is at (0, 4).
To graph this line:
- Begin by marking the point (0, 4) on the y-axis.
- To find another point using the slope, move one unit to the right to (1, 2) (since 4 - 2 = 2), and mark this point.
- Or move one unit to the left to (-1, 6) (because 4 + 2 = 6), and mark this point.
- Draw a straight line connecting these points.
**Step 3: Identifying the point of intersection**
The point of intersection of the two lines is the solution to the system of equations. The coordinates of this point are the (x, y) values that satisfy both equations simultaneously.
- By looking at the two lines drawn on the graph, you should find one point where both lines cross.
- If you plotted the lines correctly, they should intersect at the point that is the solution to the system.
**Step 4: Label and illustrate**
After plotting both lines, label each with its respective equation for clarity. Make sure your graph has labeled axes with appropriate scales to accommodate the points you've plotted. If you are graphing this on paper, use a ruler to ensure your lines are straight, and label the axes with numbers to indicate the scale.
