Converting Linear Equations: Slope-Intercept to Standard Form

What is the first step in rewriting the equation Y = 2/3x + 4/7 in standard form?

• Multiply both sides by a common multiple to eliminate fractions

• Divide both sides by a common factor

• Convert all numbers to decimals

• Add a constant to both sides

In the equation Y = 2/3x + 4/7, what does the 'm' represent in the slope-intercept form?

• The constant term

• The x-intercept

• The slope

• The y-intercept

What is the standard form of a linear equation?

• Y = mx + b

• Ax + By = C

• Ax = By + C

• y = Ax + B

Why do we need to ensure that A, B, and C in the standard form do not share a common factor?

• To make the equation more complex

• To ensure the equation is in its simplest form

• To change the slope of the line

• To make the equation easier to solve

What is the result of multiplying both sides of Y = 2/3x + 4/7 by 21?

• Y = 14x + 12

• 21Y = 2x + 4

• 21Y = 14x + 12

• Y = 2x + 4

After eliminating fractions, what is the next step in rewriting the equation in standard form?

• Divide all terms by a common factor

• Convert all numbers to decimals

• Add a constant to both sides

• Combine like terms and move them to one side

What operation is performed to move 14x to the left side of the equation?

• Addition

• Multiplication

• Subtraction

• Division

What is the simplified form of the equation after moving all terms to one side?

• 14x + 21y = 12

• Negative 14x + 21y = 12

• 21y = 14x + 12

• 14x - 21y = 12

Which of the following sets of numbers do not share a common factor?

• 4, 8, 12

• 14, 21, 12

• 6, 9, 12

• 10, 15, 20

What is the final standard form of the equation Y = 2/3x + 4/7?

• 14x + 21y = 12

• 14x - 21y = 12

• Negative 14x + 21y = 12

• 21y = 14x + 12