Algebra 1: Extra Practice - X and Y Intercepts

Overview of Intercepts

• X-Intercept: The point where the line crosses the x-axis (y=0).
• Y-Intercept: The point where the line crosses the y-axis (x=0).

Finding Intercepts

Steps to Find X and Y Intercepts

1. To find the x-intercept:

   • Set $y=0$ in the equation and solve for $x$.

2. To find the y-intercept:

   • Set $x=0$ in the equation and solve for $y$.

Example Problems

1. Equation: $4x + 5y = 20$

   • X-Intercept:
     • Setting $y=0$: $4x = 20$, thus $x=5$
     • Point: $(5, 0)$
   • Y-Intercept:
     • Setting $x=0$: $5y = 20$, thus $y=4$
     • Point: $(0, 4)$

2. Equation: $2x + y = 2$

   • X-Intercept:
     • Set $y=0$: $2x = 2$, thus $x=1$
     • Point: $(1, 0)$
   • Y-Intercept:
     • Set $x=0$: $y = 2$
     • Point: $(0, 2)$

3. Equation: $2x - y = -4$

   • X-Intercept:
     • Set $y=0$: $2x = -4$, thus $x=-2$
     • Point: $(-2, 0)$
   • Y-Intercept:
     • Set $x=0$: -y = -4
       ightarrow y=4
     • Point: $(0, 4)$

4. Equation: $x - 2y = 8$

   • X-Intercept:
     • Set $y=0$: $x = 8$
     • Point: $(8, 0)$
   • Y-Intercept:
     • Set $x=0$: -2y = 8
       ightarrow y=-4
     • Point: $(0, -4)$

Additional Equations

• Use the same method of substituting to find intercepts for the following equations:
  • $2x + y = -4$
  • $x - y = 5$
  • $x + 2y = -2$
  • $5x + 4y = 20$
  • $x + y = 5$
  • $x - y = 4$