How do you graph 2 equations and then find the common area on the graph?
To graph two equations and find their common area, you can follow these steps:
1. Start by selecting a coordinate system or grid on a piece of graph paper, or use graphing software.
2. Choose values for the x-axis (horizontal) and find the corresponding values for y-axis (vertical) using one of the equations. Repeat this step to create a set of points.
3. Plot the points on the graph by marking their intersection with the x and y-axes. Connect the points to form a line, if the equation represents a straight line. If the equation represents a curve, you may need to calculate additional points or use a graphing calculator or software to plot it accurately.
4. Repeat steps 2 and 3 for the second equation, obtaining a different set of points and plotting them.
5. Analyze the regions where the two lines or curves intersect or overlap. Identify the points of intersection as they represent the common solutions to both equations.
6. Shade or highlight the area where the two graphs overlap. This shaded region represents the common area for both equations.
Note: If the two equations are linear equations (representing straight lines), you can also find the point of intersection analytically by solving the system of equations.