Geometry For Dummies
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In coordinate geometry, there are different line equations you can use, depending on whether a line is horizontal, vertical, or at an angle, and whether you know the line's y-intercept.

Here are the basic forms for equations of lines:

  • Slope-intercept form. Use this form when you know (or can easily find) a line's slope and its y-intercept (the point where the line crosses the y-axis). y = mx + b, where m is the slope and b is the y-intercept.
  • Point-slope form. This is the easiest form to use when you don't know a line's y-intercept but you do know the coordinates of a point on the line; you also need to know the line's slope. yy1 = m(xx1), where m is the slope and (x1, y1) is a point on the line.
  • Horizontal line. This form is used for lines with a slope of zero. y = b, where b is the y-intercept. The b (or the number that's plugged into b) tells you how far up or down the line is along the y-axis. Note that every point along a horizontal line has the same y-coordinate, namely b. In case you're curious, this equation form is a special case of y = mx + b, where m = 0.
  • Vertical line. And here's the equation for a line with an undefined slope. x = a, where a is the x-intercept. The a (or the number that's plugged into a) tells you how far to the right or left the line is along the x-axis. Every point along a vertiscal line has the same x-coordinate, namely a.

Don't mix up the equations for horizontal and vertical lines. This mistake is extremely common. Because a horizontal line is parallel to the x-axis, you might think that the equation of a horizontal line would be x = a. And you might figure that the equation for a vertical line would be y = b because a vertical line is parallel to the y-axis. But as you see in the preceding equations, it's the other way around.

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Mark Ryan is the founder and owner of The Math Center in the Chicago area, where he provides tutoring in all math subjects as well as test preparation. Mark is the author of Calculus For Dummies, Calculus Workbook For Dummies, and Geometry Workbook For Dummies.

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