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Question 18604: All through the chapter in my algebra class, I have not understood the standard form of a line: Ax+By=C. I only understand slope intercept form: Y=mx+b. Could you please explain how to put the information that is given about a line ( the slope, x intercept, and y intercept)into standard form. Thank you!
Answer by mmm4444bot(95)   (Show Source):
You can put this solution on YOUR website! Hello There:
If you have a linear equation in slope-intercept form, changing the equation to standard form is as easy as moving the x-term to the other side. If any of the coefficients or the constant are fractions, then you also multiply your result by the least common multiple of the denominator(s). If, after doing these things, the coefficient on x is negative, then we also multiply both sides by -1 because standard form always has a positive coefficient on x.
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Example:
y = (7/8)*x + 2
Move the x-term to the other side by subtracting (7/8)*x from both sides.
y - (7/8)*x = 2
Multiply both sides by 8 to clear the fractions.
8*y - 7*x = 2
Multiply both sides by -1.
7*x - 8*y = -2
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Another example:
y = -(8/9)*x - (22/7)
Move the x-term to the other side by adding (8/9)*x to both sides.
(8/9)*x + y = -(22/7)
To clear the fractions, we need to multiply both sides by the least common multiple of 9 and 7. This number is 63.
56*x + 63*y = -198
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In the case where you're given the x-intercept and the y-intercept, AND THEY AER NOT ZERO, then you can use the intercept form of a linear equation:
x/a + y/b = 1
where a is the x-intercept, and b is the y-intercept.
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Example: The x-intercept is 3, and the y-intercept is 4/5.
Substituting 3 for a and 4/5 for b in the intercept form gives us the following.
x/3 + (5/4)*y = 1
Now, simply multiply both sides by 12 to clear the fractions.
4*x + 15*y = 1
~ Mark
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