Let's solve each equation by converting it from
standard form ($Ax + By = C$) to
slope-intercept form ($y = mx + b$), where $m$ is the slope and $b$ is the y-intercept.
---
1. $-2x + y = -4$
Step 1: Solve for $y$.
$$
-2x + y = -4
$$
Add $2x$ to both sides:
$$
y = 2x - 4
$$
✔ Slope-intercept form: $y = 2x - 4$
---
2. $x + 3y = 3$
Step 1: Solve for $y$.
$$
x + 3y = 3
$$
Subtract $x$ from both sides:
$$
3y = -x + 3
$$
Divide every term by 3:
$$
y = -\frac{1}{3}x + 1
$$
✔ Slope-intercept form: $y = -\frac{1}{3}x + 1$
---
3. $5x + 6y = -12$
Step 1: Solve for $y$.
$$
5x + 6y = -12
$$
Subtract $5x$ from both sides:
$$
6y = -5x - 12
$$
Divide every term by 6:
$$
y = -\frac{5}{6}x - 2
$$
✔ Slope-intercept form: $y = -\frac{5}{6}x - 2$
---
4. $4x + 3y = 3$
Step 1: Solve for $y$.
$$
4x + 3y = 3
$$
Subtract $4x$ from both sides:
$$
3y = -4x + 3
$$
Divide every term by 3:
$$
y = -\frac{4}{3}x + 1
$$
✔ Slope-intercept form: $y = -\frac{4}{3}x + 1$
---
5. $3x + y = -12$
Step 1: Solve for $y$.
$$
3x + y = -12
$$
Subtract $3x$ from both sides:
$$
y = -3x - 12
$$
✔ Slope-intercept form: $y = -3x - 12$
---
6. $4x + 7y = -14$
Step 1: Solve for $y$.
$$
4x + 7y = -14
$$
Subtract $4x$ from both sides:
$$
7y = -4x - 14
$$
Divide every term by 7:
$$
y = -\frac{4}{7}x - 2
$$
✔ Slope-intercept form: $y = -\frac{4}{7}x - 2$
---
✔ Final Answers:
| Standard Form | Slope-Intercept Form |
|---------------------------|------------------------------------|
| $-2x + y = -4$ | $y = 2x - 4$ |
| $x + 3y = 3$ | $y = -\frac{1}{3}x + 1$ |
| $5x + 6y = -12$ | $y = -\frac{5}{6}x - 2$ |
| $4x + 3y = 3$ | $y = -\frac{4}{3}x + 1$ |
| $3x + y = -12$ | $y = -3x - 12$ |
| $4x + 7y = -14$ | $y = -\frac{4}{7}x - 2$ |
---
💡
Tip: To convert from standard form to slope-intercept form:
1. Isolate $y$ on one side.
2. Divide all terms by the coefficient of $y$ (if needed).
3. Simplify.
Let me know if you'd like a visual explanation or graph!
Parent Tip: Review the logic above to help your child master the concept of standard form to slope intercept form worksheet.
