To solve the given system of equations graphically, you can follow these steps to graph each equation and find their point of intersection.
Equations to Graph:
- \( y = -\frac{3}{2}x - 6 \)
- \( y = x - 1 \)
Steps for Graphing:
Step 1: Set Up Your Axes
- Draw a horizontal line representing the y-axis and a vertical line representing the x-axis. Label your axes appropriately, and make sure to mark equal intervals for both axes.
Step 2: Graph the First Equation \( y = -\frac{3}{2}x - 6 \)
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Plot the y-intercept:
- The y-intercept is where the graph crosses the y-axis, which occurs at \( -6 \). Plot the point (0, -6) on the graph.
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Use the slope to find another point:
- The slope of this line is \( -\frac{3}{2} \), which means for every 2 units you move to the right (positive x-direction), you move down 3 units (negative y-direction).
- Starting from (0, -6):
- Move right 2 units to x = 2, and down 3 units:
- This results in the point \( (2, -9) \). Plot this point.
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Draw the line:
- Draw a straight line through the points (0, -6) and (2, -9). Extend the line in both directions.
Step 3: Graph the Second Equation \( y = x - 1 \)
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Plot the y-intercept:
- The y-intercept for this equation is \( -1 \). Plot the point (0, -1).
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Use the slope to find another point:
- The slope of this line is \( 1 \), indicating that for every 1 unit you move to the right, you move up 1 unit.
- From (0, -1):
- Move right 1 unit to x = 1, and up 1 unit:
- This results in the point \( (1, 0) \). Plot this point.
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Draw the line:
- Connect the points (0, -1) and (1, 0) with a straight line, extending it in both directions.
Step 4: Identify the Point of Intersection
- Look at your graph to see where the two lines intersect. This point represents the solution to the system of equations.
- Estimate the coordinates of the intersection. If the intersection is not clear, you can use substitution or elimination methods to find the exact coordinates.
Example of Possible Intersection
After graphing, you might find that the lines intersect at a certain point, say \( (x, y) \). You can calculate this intersection precisely by either solving the equations algebraically or reading off from the graph.
Conclusion
By following these steps, you'll be able to graph the given equations and identify the point where they intersect, which will be the solution to the system of equations.
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