Converting Equations to Standard Form

The video tutorial explains how to convert equations into standard form, which is expressed as AX + BY = C, where A, B, and C are integers. It covers methods to eliminate fractions by multiplying through by a common denominator and handling decimals by converting them to integers. The tutorial also discusses rearranging terms to ensure all variables are on one side of the equation and making the leading coefficient positive if necessary. The process is demonstrated with examples, emphasizing the importance of having integer coefficients in the final standard form.

What is the standard form of a linear equation?

• x^2 + y^2 = r^2

• Ax + By = C

• y = ax^2 + bx + c

• y = mx + b

What does the equation Ax + By = C represent?

• An exponential equation

• A circle equation

• A linear equation in standard form

• A quadratic equation

Which of the following is NOT an integer?

• 7

• 5

• -3

• 0.5

Why is it important to have integer coefficients in standard form?

• To make the equation easier to graph

• To simplify calculations

• To ensure the equation is linear

• To avoid fractions and decimals

How can you eliminate fractions in an equation?

• Divide by the fraction

• Subtract the fraction from both sides

• Multiply by the least common denominator

• Add a constant to both sides

What is the next step after eliminating fractions to achieve standard form?

• Add all terms to one side

• Multiply by a negative number

• Divide by the coefficient of x

• Square both sides

Why might you multiply an equation by -1?

• To eliminate decimals

• To solve for y

• To make the leading coefficient positive

• To simplify the equation

What happens to the equation when you multiply by -1?

• The equation becomes quadratic

• The equation is solved for y

• The signs of all terms are reversed

• The equation becomes a fraction

How do you handle decimals in an equation to convert it to standard form?

• Add decimals to both sides

• Multiply by 10 or 100

• Divide by the decimal

• Subtract decimals from both sides

What is the first step in converting an equation with decimals to standard form?

• Divide by the decimal

• Subtract the decimal from both sides

• Multiply by the deepest decimal

• Add a constant to both sides