Final answer:
To convert equations to standard form Ax + By = C, move all terms to the left side of the equation and make sure A is positive. a) y = 2x + 3 becomes -y + 2x = -3; b) 3y - 5x = 7 becomes 5x + 3y = 7; c) 4x - 2y = 8 remains as 4x - 2y = 8; d) -2y + 6 = 4x becomes 4x + 2y = 6.
Step-by-step explanation:
a) Convert y = 2x + 3 to standard form:
To convert the equation y = 2x + 3 to standard form Ax + By = C, we need to move all terms to the left side of the equation and make sure that A is positive.
Start by subtracting 2x from both sides: -2x + y = 3. Next, rearrange the equation to align the terms in standard form: y - 2x = 3. Multiply through by -1 to make A positive: -y + 2x = -3. So, the standard form of the equation y = 2x + 3 is -y + 2x = -3.
b) Rewrite 3y - 5x = 7 in standard form:
To write the equation 3y - 5x = 7 in standard form Ax + By = C, we need to move all terms to the left side of the equation and make sure that A is positive.
Add 5x to both sides of the equation: 5x + 3y = 7. So, the standard form of the equation 3y - 5x = 7 is 5x + 3y = 7.
c) Transform 4x - 2y = 8 to standard form:
To transform the equation 4x - 2y = 8 to standard form Ax + By = C, we need to move all terms to the left side of the equation and make sure that A is positive.
Add 2y to both sides of the equation: 4x = 2y + 8. Rearrange the equation to align the terms in standard form: 4x - 2y = 8. So, the standard form of the equation 4x - 2y = 8 is 4x - 2y = 8.
d) Convert -2y + 6 = 4x to standard form:
To convert the equation -2y + 6 = 4x to standard form Ax + By = C, we need to move all terms to the left side of the equation and make sure that A is positive.
Subtract 4x from both sides of the equation: -4x - 2y + 6 = 0. Rearrange the equation to align the terms in standard form: -4x - 2y = -6. Multiply through by -1 to make A positive: 4x + 2y = 6. So, the standard form of the equation -2y + 6 = 4x is 4x + 2y = 6.