# 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**- 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].

- Find a third solution to the equation.
- Plot the three points and then check that they line up.
- Draw the line.

- Find the
**Choose the most convenient method to graph a line**

- 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].

- 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. - 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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- Prealgebra.
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