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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**: \(y = -\frac{7}{3}x + 6\)

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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 \(y\).

Convert the equations from standard form to slope-intercept form.

Learn how to convert linear equations from standard form (Ax + By = C) to slope-intercept form (y = mx + b) with step-by-step explanations. This worksheet covers key algebraic skills for students in Grades 7-10.

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