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Study Guides > ALGEBRA / TRIG I

Summary: Using Intercepts to Graph Lines

Key Concepts

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

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