SOLUTION: When graphing linear equations, why the line x=4 is a vertical line?
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Question 211798: When graphing linear equations, why the line x=4 is a vertical line?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the general form of the equaion of a straight line is:
ax + by = c
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a is the coefficient of the x term.
b is the coefficient of the y term.
c is the constant
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the line will be vertical when b = 0
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when b = 0, the y variable drops out of the equation and the equation becomes:
ax = c
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if you divide both sides of the equation by a, you get:
x = c/a
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you derive the slope intercept form of the straight line from the standard form of the straight line as follows:
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ax + by = c
subtract ax from both sides to get:
by = -ax + c
divide both sides by b to get:
y = -ax/b + c/b
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this can be written as:
y = (-a/b)*x + (c/b)
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the line is vertical when b = 0
you can see that when the line is vertical, the slope is undefined and the y intercept is undefined.
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a good website that addresses the standard equation of the line is found here:
http://www.analyzemath.com/line/line.htm
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they also have an interactive demonstration where you can vary the parameters of a, b, and c to see the effect on the line.
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there are sliders to the left of the graph that you move to change the value of a, b, or c.
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