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.

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.