Graphing Straight Lines Using Intercepts

Key Concepts

• To graph a straight line using intercepts, find two points where the line cuts the x-axis and the y-axis.
• Y-intercept: Set ( x = 0 ) and solve for ( y ).
• X-intercept: Set ( y = 0 ) and solve for ( x ).

Steps to Graph a Line

1. Find Y-Intercept:
   • Set ( x = 0 ) in the equation and solve for ( y ).
   • Example: For ( 2x + y = 4 ), setting ( x = 0 ) gives ( y = 4 ) (point ( (0, 4) )).
2. Find X-Intercept:
   • Set ( y = 0 ) in the equation and solve for ( x ).
   • Example: For ( 2x + y = 4 ), setting ( y = 0 ) gives ( x = 2 ) (point ( (2, 0) )).
3. Plot Points: Plot the identified intercepts on a graph.
4. Draw Line: Connect the points with a straight line.
5. Label the Graph: Always label the graph with the equation of the line.

Examples

Example 1: ( 2x + y = 4 )

• Y-intercept: ( (0, 4) )
• X-intercept: ( (2, 0) )
• Draw a line through these points and label the graph.

Example 2: ( y = 3x - 6 )

• Y-intercept: Set ( x = 0 ): ( y = -6 ) (point ( (0, -6) )).
• X-intercept: Set ( y = 0 ): ( x = 2 ) (point ( (2, 0) )).
• Plot and draw the line through these points.

Example 3: ( y = 2x )

• Origin as Intercept: ( (0, 0) ) is both the x and y-intercept.
• Find Another Point: Choose ( x = 3 ), then ( y = 6 ) (point ( (3, 6) )).
• Plot these points and draw the line through them.

Conclusion

• Practice with more examples to master graphing using intercepts.
• Remember to always label your graph with the equation of the line.

Good luck with your practice questions!