![]() There are other forms used to represent linear equations as well, but these are a few of the most commonly used in algebra. Unlike point-slope and slope-intercept form, standard form can be used to represent the equation of a vertical line, since it does not involve the use of the slope of the line. ![]() Standard form is useful for solving systems of linear equations. The standard form for the equation of a line is expressed as Like point-slope form, one of the disadvantages of slope-intercept form is that vertical lines cannot be represented in slope-intercept form since the slope of a vertical line is undefined. Often, the equation of a line in other forms is converted to slope-intercept form because of how convenient it is to work with. It is useful because given a slope and y-intercept, it is easy to write the equation of a line in slope-intercept form, as well as graph it. It is the special case of point-slope form given that the point on the line is also the y-intercept. It is similar to point-slope form except that it involves the slope of a line and its y-intercept, rather than the slope of a line and a point on the line. Where m is the slope, and b is the y-intercept. Example: A line is inclined at an angle of 60° to the horizontal, and passes through the point (0, - 1). Step 2: Apply the slope intercept formula: y mx + b. Slope-intercept form is the most commonly used form for the equation of a line, and is expressed as We can apply the slope formula to find the slope of any straight line, in case it is not given directly and other relevant data is provided. Other commonly used forms include slope-intercept form and standard form. One of the drawbacks of point-slope form is that it cannot be used to represent the equation of a vertical line, since vertical lines have undefined slopes. In such cases, point-slope form makes it easy to come up with an equation of a line and graph it. As mentioned above, point-slope form is most useful when one point on a line as well as the slope of the line are known. Point-slope form is just one of a number of different forms of a linear equation, all of which have different uses depending on the context. In the example above, we used the point (3, 7) to write the linear equation, but we also could have used (-5, 3), in which case the equation of the line would be expressed as:īoth equations represent the same line, and when writing an equation in point-slope form, the decision of which point to use is entirely up to you. We need both points in order to calculate the slope, but only one of the points to write the linear equation. ![]() Note that in the example above, we can write the equation in point-slope form using either of the two known points.
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