Question

1. $8x - 4y = 20$
2. $2x + 3y = 12$
3. $2x + y = -11$
4. $3y = 4x - 27$
5. $x - 4y = 8$
6. $y + 9 = 2(x + 5)$
7. $4x - 2y = 12$
8. $y - 1 = \frac{2}{3}(x + 3)$

Explanation:

Assuming the task is to rewrite these linear equations in slope - intercept form ($y = mx + b$, where $m$ is the slope and $b$ is the y - intercept), we will solve each equation one by one:

Equation 7: $8x - 4y = 20$

Step 1: Isolate the $y$ - term

Subtract $8x$ from both sides of the equation:
$-4y=-8x + 20$

Step 2: Solve for $y$

Divide each term by $-4$:
$y=\frac{-8x}{-4}+\frac{20}{-4}$
$y = 2x-5$

Equation 8: $2x + 3y = 12$

Step 1: Isolate the $y$ - term

Subtract $2x$ from both sides:
$3y=-2x + 12$

Step 2: Solve for $y$

Divide each term by $3$:
$y=\frac{-2x}{3}+\frac{12}{3}$
$y=-\frac{2}{3}x + 4$

Equation 9: $2x + y=-11$

Step 1: Solve for $y$

Subtract $2x$ from both sides:
$y=-2x-11$

Equation 10: $3y = 4x - 27$

Step 1: Solve for $y$

Divide each term by $3$:
$y=\frac{4x}{3}-\frac{27}{3}$
$y=\frac{4}{3}x-9$

Equation 11: $x - 4y = 8$

Step 1: Isolate the $y$ - term

Subtract $x$ from both sides:
$-4y=-x + 8$

Step 2: Solve for $y$

Divide each term by $-4$:
$y=\frac{-x}{-4}+\frac{8}{-4}$
$y=\frac{1}{4}x-2$

Equation 12: $y + 9 = 2(x + 5)$

Step 1: Expand the right - hand side

$y + 9 = 2x+10$

Step 2: Solve for $y$

Subtract $9$ from both sides:
$y=2x + 10 - 9$
$y=2x+1$

Equation 13: $4x - 2y = 12$

Step 1: Isolate the $y$ - term

Subtract $4x$ from both sides:
$-2y=-4x + 12$

Step 2: Solve for $y$

Divide each term by $-2$:
$y=\frac{-4x}{-2}+\frac{12}{-2}$
$y = 2x-6$

Equation 14: $y - 1=\frac{2}{3}(x + 3)$

Step 1: Expand the right - hand side

$y - 1=\frac{2}{3}x+2$

Step 2: Solve for $y$

Add $1$ to both sides:
$y=\frac{2}{3}x+2 + 1$
$y=\frac{2}{3}x+3$

If you want to solve these equations for specific values (e.g., find the intersection point of two lines) or perform other operations, please provide more specific instructions.

If we consider the general form of converting to slope - intercept form:

1. $y = 2x-5$

1. $y=-\frac{2}{3}x + 4$

1. $y=-2x-11$

1. $y=\frac{4}{3}x-9$

1. $y=\frac{1}{4}x-2$

1. $y=2x+1$

1. $y = 2x-6$

1. $y=\frac{2}{3}x+3$

Answer:

Assuming the task is to rewrite these linear equations in slope - intercept form ($y = mx + b$, where $m$ is the slope and $b$ is the y - intercept), we will solve each equation one by one:

Equation 7: $8x - 4y = 20$

Step 1: Isolate the $y$ - term

Subtract $8x$ from both sides of the equation:
$-4y=-8x + 20$

Step 2: Solve for $y$

Divide each term by $-4$:
$y=\frac{-8x}{-4}+\frac{20}{-4}$
$y = 2x-5$

Equation 8: $2x + 3y = 12$

Step 1: Isolate the $y$ - term

Subtract $2x$ from both sides:
$3y=-2x + 12$

Step 2: Solve for $y$

Divide each term by $3$:
$y=\frac{-2x}{3}+\frac{12}{3}$
$y=-\frac{2}{3}x + 4$

Equation 9: $2x + y=-11$

Step 1: Solve for $y$

Subtract $2x$ from both sides:
$y=-2x-11$

Equation 10: $3y = 4x - 27$

Step 1: Solve for $y$

Divide each term by $3$:
$y=\frac{4x}{3}-\frac{27}{3}$
$y=\frac{4}{3}x-9$

Equation 11: $x - 4y = 8$

Step 1: Isolate the $y$ - term

Subtract $x$ from both sides:
$-4y=-x + 8$

Step 2: Solve for $y$

Divide each term by $-4$:
$y=\frac{-x}{-4}+\frac{8}{-4}$
$y=\frac{1}{4}x-2$

Equation 12: $y + 9 = 2(x + 5)$

Step 1: Expand the right - hand side

$y + 9 = 2x+10$

Step 2: Solve for $y$

Subtract $9$ from both sides:
$y=2x + 10 - 9$
$y=2x+1$

Equation 13: $4x - 2y = 12$

Step 1: Isolate the $y$ - term

Subtract $4x$ from both sides:
$-2y=-4x + 12$

Step 2: Solve for $y$

Divide each term by $-2$:
$y=\frac{-4x}{-2}+\frac{12}{-2}$
$y = 2x-6$

Equation 14: $y - 1=\frac{2}{3}(x + 3)$

Step 1: Expand the right - hand side

$y - 1=\frac{2}{3}x+2$

Step 2: Solve for $y$

Add $1$ to both sides:
$y=\frac{2}{3}x+2 + 1$
$y=\frac{2}{3}x+3$

If you want to solve these equations for specific values (e.g., find the intersection point of two lines) or perform other operations, please provide more specific instructions.

If we consider the general form of converting to slope - intercept form:

1. $y = 2x-5$

1. $y=-\frac{2}{3}x + 4$

1. $y=-2x-11$

1. $y=\frac{4}{3}x-9$

1. $y=\frac{1}{4}x-2$

1. $y=2x+1$

1. $y = 2x-6$

1. $y=\frac{2}{3}x+3$