To convert these equations from standard form ($Ax + By = C$) to slope-intercept form ($y = mx + b$), we'll solve each equation for $y$ in terms of $x$. Here are the steps for each problem:

Problem 5: $2x - y = -7$

1. Start with the equation:
   $2x - y = -7$

2. Isolate $y$ by moving $2x$ to the other side:
   $-y = -2x - 7$

3. Divide by $-1$ to solve for $y$:
   $y = 2x + 7$

Solution: $y = 2x + 7$

Problem 6: $5x + 3y = 12$

1. Start with the equation:
   $5x + 3y = 12$

2. Isolate $3y$ by moving $5x$ to the other side:
   $3y = -5x + 12$

3. Divide by $3$ to solve for $y$:
   $y = -\frac{5}{3}x + 4$

Solution: $y = -\frac{5}{3}x + 4$

Problem 7: $x - y = 1$

1. Start with the equation:
   $x - y = 1$

2. Isolate $-y$ by moving $x$ to the other side:
   $-y = -x + 1$

3. Divide by $-1$ to solve for $y$:
   $y = x - 1$

Solution: $y = x - 1$

Problem 8: $x - 3y = -15$

1. Start with the equation:
   $x - 3y = -15$

2. Isolate $-3y$ by moving $x$ to the other side:
   $-3y = -x - 15$

3. Divide by $-3$ to solve for $y$:
   $y = \frac{1}{3}x + 5$

Solution: $y = \frac{1}{3}x + 5$

Problem 9: $8x - 10y = 20$

1. Start with the equation:
   $8x - 10y = 20$

2. Isolate $-10y$ by moving $8x$ to the other side:
   $-10y = -8x + 20$

3. Divide by $-10$ to solve for $y$:
   $y = \frac{4}{5}x - 2$

Solution: $y = \frac{4}{5}x - 2$

Problem 10: $14x + 6y = 36$

1. Start with the equation:
   $14x + 6y = 36$

2. Isolate $6y$ by moving $14x$ to the other side:
   $6y = -14x + 36$

3. Divide by $6$ to solve for $y$:
   $y = -\frac{7}{3}x + 6$

Solution: $y = -\frac{7}{3}x + 6$

Would you like further explanation on any of these steps?

Related Questions:

1. How do you convert from slope-intercept form back to standard form?
2. What does the slope of each equation represent?
3. How can you identify the y-intercept from the slope-intercept form?
4. How can you graph an equation once it’s in slope-intercept form?
5. Why is slope-intercept form useful for analyzing linear equations?

Tip:

To quickly convert equations to slope-intercept form, remember that you just need to isolate $y$ by moving other terms to the opposite side and dividing by the coefficient of $y$.