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Recall that you can draw a line on the coordinate plane if you know the right information. That is, if you know either:
1. The coordinates of two points that lie on the line or 2. The coordinate of one point that lies on the line and the slope of the line. Let's look at examples that demonstrate each case.
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EXAMPLE 1: | EXAMPLE 2: | ||||
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Mark these two points on the plane. | Mark the point | ||||
Draw the line passing through these two points. | Draw the line passing through these two points. | ||||
Given a point on a line and the slope of the line, you can write the equation of a line using the point-slope equation:
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Let's now write the equations of the lines drawn Examples 1 and 2. |
EXAMPLE 1: | EXAMPLE 2: | |||||||||||||||||||||
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You can compute the slope of this line using the slope equation:
Recall that the two points were
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For this example, you are given the slope of the line, | |||||||||||||||||||||
Check with the above graph to verify that the slope is | ||||||||||||||||||||||
You now have enough information to fill in the point-slope formula: | Enter this information into the point-slope formula. Recall that the point given was | |||||||||||||||||||||
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The equation of the line is | The equation of the line is |
In both examples, we arrived at an equation of the form Note that if you let | Since it is easy to pick out the y-intercept and slope in the this equation, it is often referred to as the slope-intercept equation.
| Note that if you know the y-intercept and slope of a line, you can write the equation of the line by entering the appropriate values for m and b in the slope-intercept equation.
| Any linear equation can be rewritten into a general equation of the form
| Let's write the linear equations from the examples in general form.
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EXAMPLE 1: | EXAMPLE 2: |
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-(1/4)x - y + 1 = 0 or, multiplying both sides by -4 gives, x + 4y - 4 = 0 3x - y + 6 = 0 |
Go to this page, where you will find an action figure and some questions which will test your skill at writing linear equations. |