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Liula [17]
3 years ago
10

A line has the equation y = 1/2x + 3. Convert this equation to standard form and write another equation that will have the same

graph.​
Mathematics
1 answer:
Ivenika [448]3 years ago
4 0

Equation of a line in standard form is Ax + By = C

A is a pos. integer and B + C are integers

1) multiply all terms in the equation by 2

2y = x - 6

2) subtract 2y from both sides

2y - 2y (cancelled out) = x - 2y - 6

x - 2y - 6 = 0

3) add 6 to both sides

x-2y = 0 +6 (-6 and +6 cancel out)

therefore,

x - 2y = 6

is the equation in standard form

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Answer:

\large\boxed{x=\dfrac{85}{24}=3\dfrac{13}{24}}

Step-by-step explanation:

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3\dfrac{1}{8}=\dfrac{3\cdot8+1}{8}=\dfrac{25}{8}

METHOD 1:

x-3\dfrac{1}{8}=\dfrac{5}{12}\\\\x-\dfrac{25}{8}=\dfrac{5}{12}\\\\\text{the common denominator is 24}\\\\x-\dfrac{25}{8}=\dfrac{5}{12}\qquad\text{multiply both sides by 24}\\\\24x-(3)(25)=(2)(5)\\\\24x-75=10\qquad\text{add 75 to both sides}\\\\24x=85\qquad\text{divide both sides by 24}\\\\\boxed{x=\dfrac{85}{24}}

METHOD 2:

x-3\dfrac{1}{8}=\dfrac{5}{12}\qquad\text{add}\ 3\dfrac{1}{8}\ \text{to oboth sides}\\\\x=\dfrac{5}{12}+3\dfrac{1}{8}\\\\x=\dfrac{5\cdot2}{12\cdot2}+3\dfrac{1\cdot3}{8\cdot3}\\\\x=\dfrac{10}{24}+3\dfrac{3}{24}\\\\x=3\dfrac{10+3}{24}\\\\\boxed{x=3\dfrac{13}{24}}

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