Key Concepts

Key Concepts

• Find the x- and y- Intercepts from the Equation of a Line
  
  • Use the equation of the line to find the x- intercept of the line, let \(y=0\) and solve for x.
  • Use the equation of the line to find the y- intercept of the line, let \(x=0\) and solve for y.
• Graph a Linear Equation 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.
• Strategy for Choosing the Most Convenient Method to Graph a Line:
  
  • Consider the form of the equation.
  • If it only has one variable, it is a vertical or horizontal line.
    \(x=a\) is a vertical line passing through the x- axis at \(a\)
    \(y=b\) is a horizontal line passing through the y- axis at \(b\).
  • If y is isolated on one side of the equation, graph by plotting points.
  • Choose any three values for x and then solve for the corresponding y- values.
  • 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

The points where a line crosses the $x$- axis and the $y$- axis are called the intercepts of the line.

$x$- intercept

The point $(a,0)$ where the line crosses the $x$- axis; the $x$- intercept occurs when $y$ is zero.

$y$-intercept

The point $(0,b)$ where the line crosses the $y$- axis; the $y$- intercept occurs when $x$ is zero.