Determining Intercepts of a Line

Introduction

• Objective: Find the x-intercept and y-intercept of a line given its equation.
• Method: Use a special table of values to determine intercepts.

Concept Explanation

• X-axis: Every y-coordinate is 0.
• Y-axis: Every x-coordinate is 0.

Steps to Determine Intercepts

X-intercept

1. Set y = 0 and solve for x.
2. Example:
   • Given equation: (2x + y = 5)
   • Set (y = 0):
     • Equation becomes (2x = 5).
     • Solve: (x = \frac{5}{2}).
   • X-intercept point: (\left(\frac{5}{2}, 0\right)) or (2.5, 0).

Y-intercept

1. Set x = 0 and solve for y.
2. Example:
   • Given equation: (2x + y = 5)
   • Set (x = 0):
     • Equation becomes (-y = 5).
     • Solve: (y = -5).
   • Y-intercept point: ((0, -5)).

Important Notes

• Do not list intercepts as just numbers (e.g., x = 5/2), because it implies a vertical or horizontal line.
• Always provide intercepts as ordered pairs.

Plotting and Sketching

• X-intercept: (\left(\frac{5}{2}, 0\right)) or (2.5, 0).
• Y-intercept: ((0, -5)).
• Sketch the line passing through these two points.

Conclusion

• This method helps determine and plot the intercepts of a line, facilitating a better understanding of linear equations.
• Always express intercepts as ordered pairs to avoid confusion.

End of Lecture