Linear Algebra For Dummies
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You can use the slope-intercept form to graph inequalities. The slope-intercept form is expressed as y = mx + b, where the variable m stands for the slope of the line, and b stands for the y-intercept (or where the line crosses the y-axis).

You can change equations that aren’t written in slope-intercept form by solving for y. For example, graphing 2x – 3y = 12 requires you to subtract 2x from both sides first to get –3y = –2x + 12. Then you divide every term by –3 to get

y equals two thirds of x plus four.

This graph starts at (0,–4) on the y-axis; to find the next point, you move up two and right three (using the slope). This gets you to the point (3,-2). Slope is often expressed as a fraction because it’s rise over run — in this case 2/3.

Inequalities are used for comparisons, which are a big part of pre-calculus. They show a relationship between two expressions (greater than, less than, or equal to). Graphing inequalities starts exactly the same as graphing equalities, but at the end of the graphing process (you still put the equation in slope-intercept form and graph), you have two decisions to make:

  • Is the line dashed, meaning y < mx+b or y > mx+b, or is the line solid, meaning

    y < mx+b or y > mx+b
  • Do you shade under the line

    y < mx+b or y _< mx+b

    or do you shade above the line

    y > mx+b or y >_ mx+b

For inequalities, you show all possible solutions by shading the side of line that works in the original equation.

For example, when graphing y < 2x – 5, you follow these steps:

  1. Start off at –5 on the y-axis and mark a point.

  2. Move up two and right one to find a second point.

  3. When connecting the dots, you produce a straight dashed line.

  4. Shade on the bottom half of the graph to show all possible points in the solution.

About This Article

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Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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