Summary: Using Intercepts to Graph Lines

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.
• 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].
• 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. Then 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 or the [latex]y[/latex]-axis is called an intercept of the line.

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