To convert an equation from standard form ($Ax + By = C$) to slope-intercept form ($y = mx + b$), the goal is to get $y$ by itself on one side of the equal sign.
Here are the step-by-step solutions for each problem:
1. $-2x + y = -4$
* Add $2x$ to both sides to isolate $y$.
* $y = 2x - 4$
2. $x + 3y = 3$
* Subtract $x$ from both sides: $3y = -x + 3$
* Divide every term by 3: $y = \frac{-1}{3}x + \frac{3}{3}$
* Simplify: $y = -\frac{1}{3}x + 1$
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: $y = -\frac{5}{6}x - 2$
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: $y = -\frac{4}{3}x + 1$
5. $3x + y = -12$
* Subtract $3x$ from both sides to isolate $y$.
* $y = -3x - 12$
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: $y = -\frac{4}{7}x - 2$
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. $y = -\frac{4}{7}x - 2$
Parent Tip: Review the logic above to help your child master the concept of slope intercept form to standard form worksheet.
