Mathematics » Introducing Graphs » Graphing with Intercepts

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.
      xy
       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.

Glossary

intercepts of a line

Each of the points at which a line crosses the x-axis and the y-axis is called an intercept of the line.

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