Key Concepts

Key Concepts

• Intercepts
  • The x-intercept is the point, \(\left(a,0\right)\), where the graph crosses the x-axis. The x-intercept occurs when y is zero.
  • The y-intercept is the point, \(\left(0,b\right)\), where the graph crosses the y-axis. The y-intercept occurs when y is zero.
  • The x-intercept occurs when y is zero.
  • The y-intercept occurs when x is zero.
• Find the x and y intercepts from the equation of a line
  • To find the x-intercept of the line, let \(y=0\) and solve for x.
  • To find the y-intercept of the line, let \(x=0\) and solve for y.
    

    x	y
    	0
    0

• Graph a line using the intercepts
  1. Find the x- and y- intercepts of the line.
     • Let \(y=0\) and solve for x.
     • Let \(x=0\) and solve for y.
  2. Find a third solution to the equation.
  3. Plot the three points and then check that they line up.
  4. Draw the line.
• Choose the most convenient method to graph a line
  1. Determine if the equation has only one variable. Then it is a vertical or horizontal line.
      

     \(x=a\) is a vertical line passing through the x-axis at a.

      

     \(y=b\) is a vertical line passing through the y-axis at b.

  2. Determine if y is isolated on one side of the equation. The graph by plotting points.
      

     Choose any three values for x and then solve for the corresponding y- values.

  3. Determine if the equation is of the form \(Ax+By=C\), find the intercepts.
      

     Find the x- and y- intercepts and then a third point.