Summary: Plotting Lines on the Rectangular Coordinate System

Key Concepts

  • Intercepts
    • The [latex]x[/latex]-intercept is the point, [latex]\left(a,0\right)[/latex] , where the graph crosses the [latex]x[/latex]-axis. The [latex]x[/latex]-intercept occurs when [latex]y[/latex] is zero.
    • The [latex]y[/latex]-intercept is the point, [latex]\left(0,b\right)[/latex] , where the graph crosses the [latex]y[/latex]-axis. The [latex]y[/latex]-intercept occurs when [latex]y[/latex] is zero.
    • The [latex]x[/latex]-intercept occurs when [latex]y[/latex] is zero.
    • The [latex]y[/latex]-intercept occurs when [latex]x[/latex] is zero.
  • Find the x and y intercepts from the equation of a line
    • To find the [latex]x[/latex]-intercept of the line, let [latex]y=0[/latex] and solve for [latex]x[/latex].
    • To find the [latex]y[/latex]-intercept of the line, let [latex]x=0[/latex] and solve for [latex]y[/latex].
      [latex]x[/latex] [latex]y[/latex]
      [latex]0[/latex]
      [latex]0[/latex]
  • Graph a line using the intercepts
    1. Find the x- and y- intercepts of the line.
      • Let [latex]y=0[/latex] and solve for [latex]x[/latex].
      • Let [latex]x=0[/latex] and solve for [latex]y[/latex].
    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.
    • [latex]x=a[/latex] is a vertical line passing through the [latex]x[/latex]-axis at [latex]a[/latex].
    • [latex]y=b[/latex] is a vertical line passing through the [latex]y[/latex]-axis at [latex]b[/latex].
  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 [latex]Ax+By=C[/latex] , 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 [latex]x[/latex]-axis and the [latex]y[/latex]-axis is called an intercept of the line.