Convert linear equations from standard form to slope-intercept form on this math worksheet.

To convert an equation from standard form ($Ax + By = C$) to slope-intercept form ($y = mx + b$), we need to isolate $y$ on one side of the equal sign. This means getting $y$ by itself.

Here is the step-by-step solution for each problem:

1. $-2x + y = -4$
* Add $2x$ to both sides to move the $x$ term.
* $y = 2x - 4$

2. $x + 3y = 3$
* Subtract $x$ from both sides: $3y = -x + 3$
* Divide every term by 3 to get $y$ by itself:
* $y = -\frac{1}{3}x + \frac{3}{3}$
* Simplify the fraction: $y = -\frac{1}{3}x + 1$

3. $5x + 6y = -12$
* Subtract $5x$ from both sides: $6y = -5x - 12$
* Divide every term by 6:
* $y = -\frac{5}{6}x - \frac{12}{6}$
* Simplify the fraction: $y = -\frac{5}{6}x - 2$

4. $4x + 3y = 3$
* Subtract $4x$ from both sides: $3y = -4x + 3$
* Divide every term by 3:
* $y = -\frac{4}{3}x + \frac{3}{3}$
* Simplify the fraction: $y = -\frac{4}{3}x + 1$

5. $3x + y = -12$
* Subtract $3x$ from both sides. Since $y$ has no number in front of it, you don't need to divide.
* $y = -3x - 12$

6. $4x + 7y = -14$
* Subtract $4x$ from both sides: $7y = -4x - 14$
* Divide every term by 7:
* $y = -\frac{4}{7}x - \frac{14}{7}$
* Simplify the fraction: $y = -\frac{4}{7}x - 2$

Final Answer:
1. $y = 2x - 4$
2. $y = -\frac{1}{3}x + 1$
3. $y = -\frac{5}{6}x - 2$
4. $y = -\frac{4}{3}x + 1$
5. $y = -3x - 12$
6. $y = -\frac{4}{7}x - 2$