Converting to Standard Form

This video tutorial explains the equation of a line in standard form, ax + by + c = 0, and how to convert between this form and the slope-intercept form, y = mx + b. It covers the restrictions on the coefficients a, b, and c, emphasizing that a must be a positive integer, while b and c must be integers. The tutorial provides examples of converting equations with and without fractions, ensuring the correct order of terms and positive coefficients. It also demonstrates converting from standard form back to slope-intercept form, focusing on isolating the y variable.

What is the standard form of a line equation?

• y = ax^2 + bx + c

• ax^2 + bx + c = 0

• y = mx + b

• ax + by + c = 0

Which of the following is a restriction on the coefficient 'a' in the standard form?

• It must be a negative integer.

• It must be a positive integer.

• It can be a fraction.

• It can be a decimal.

In the equation 3x + 5y - 7 = 0, what is the value of 'c'?

• -7

• 5

• 0

• 3

How do you convert y = 2x + 5 to standard form?

• Multiply by 2.

• Subtract 2x from both sides.

• Add y to both sides.

• Subtract y from both sides.

What should you do if the 'a' value is negative in the standard form?

• Leave it as is.

• Multiply the entire equation by -1.

• Add 1 to 'a'.

• Subtract 1 from 'a'.

When converting y = -2x - 7 to standard form, what is the first step?

• Multiply by -1.

• Subtract y from both sides.

• Add 7 to both sides.

• Add 2x to both sides.

How do you handle fractions in the coefficients when converting to standard form?

• Add the fractions together.

• Convert fractions to decimals.

• Ignore the fractions.

• Multiply by the lowest common multiple of the denominators.

What is the lowest common multiple of 7 and 14?

• 7

• 14

• 21

• 28

To convert from standard form to slope-intercept form, what is the first step?

• Add c to both sides.

• Multiply by -1.

• Isolate the y variable.

• Isolate the x variable.

In the equation 9x - 4y + 19 = 0, what is the first step to convert it to y = mx + b?

• Add 4y to both sides.

• Add 19 to both sides.

• Subtract 9x from both sides.

• Divide by 4.