Standard Form and Linear Equations

The video tutorial explains how to convert an equation from slope-intercept form to standard form. It begins by defining both forms and then demonstrates the process of rearranging terms to achieve the standard form. The tutorial emphasizes the importance of having all terms on one side and ensuring the equation is simplified by factoring out common factors. The final equation is presented in its simplest standard form, with a review of key points to ensure understanding.

What is the standard form of a linear equation?

• y = mx + b

• x = ay + b

• ax + by = c

• y = ax + c

What is the slope-intercept form of a linear equation?

• x = ay + b

• y = mx + b

• ax + by = c

• y = ax + c

In the equation 6y + 8x = 14, what is the first step to convert it to standard form?

• Add 8x to both sides

• Multiply both sides by 2

• Divide both sides by 6

• Subtract 8x from both sides

Why do we subtract 14 from both sides in the equation?

• To isolate y

• To isolate x

• To set the equation to zero

• To simplify the equation

What is the main goal when converting an equation to standard form?

• To eliminate constants

• To have x and y on the same side

• To isolate x

• To isolate y

What is the result of subtracting 8x from both sides of the equation?

• 8x is halved

• 8x is doubled

• 8x is eliminated from one side

• 8x is added to both sides

What is the purpose of factoring out common factors in an equation?

• To make the equation more complex

• To simplify the equation

• To eliminate variables

• To change the equation's form

Which number is a common factor in the equation -8x - 6y = -14?

• 5

• 2

• 4

• 3

What is the simplest form of the equation after factoring out the common factor?

• -2x - 3y = -7

• -4x - 3y = -7

• -8x - 6y = -14

• -4x - 6y = -7

What condition must be met for an equation to be in standard form?

• No common factor greater than one

• All coefficients must share a common factor greater than one

• All terms must be on one side

• All coefficients must be positive