Let's solve each problem by converting the
standard form of a linear equation to
slope-intercept form, which is:
$$
y = mx + b
$$
where:
- $ m $ is the slope,
- $ b $ is the y-intercept.
We'll isolate $ y $ on one side of the equation.
---
1. Standard form: $ 10x - 7y = -8 $
Solve for $ y $:
$$
-7y = -10x - 8
$$
Divide both sides by $-7$:
$$
y = \frac{10}{7}x + \frac{8}{7}
$$
✔ Slope-intercept form: $ y = \frac{10}{7}x + \frac{8}{7} $
---
2. Standard form: $ 8x + y = 9 $
Solve for $ y $:
$$
y = -8x + 9
$$
✔ Slope-intercept form: $ y = -8x + 9 $
---
3. Standard form: $ x + 6y = -2 $
Solve for $ y $:
$$
6y = -x - 2
$$
$$
y = -\frac{1}{6}x - \frac{1}{3}
$$
✔ Slope-intercept form: $ y = -\frac{1}{6}x - \frac{1}{3} $
---
4. Standard form: $ 4x + 3y = 9 $
Solve for $ y $:
$$
3y = -4x + 9
$$
$$
y = -\frac{4}{3}x + 3
$$
✔ Slope-intercept form: $ y = -\frac{4}{3}x + 3 $
---
5. Standard form: $ 3x + 12y = -8 $
Solve for $ y $:
$$
12y = -3x - 8
$$
$$
y = -\frac{3}{12}x - \frac{8}{12} = -\frac{1}{4}x - \frac{2}{3}
$$
✔ Slope-intercept form: $ y = -\frac{1}{4}x - \frac{2}{3} $
---
6. Standard form: $ x + 2y = -8 $
Solve for $ y $:
$$
2y = -x - 8
$$
$$
y = -\frac{1}{2}x - 4
$$
✔ Slope-intercept form: $ y = -\frac{1}{2}x - 4 $
---
7. Standard form: $ 11x - 8y = 3 $
Solve for $ y $:
$$
-8y = -11x + 3
$$
$$
y = \frac{11}{8}x - \frac{3}{8}
$$
✔ Slope-intercept form: $ y = \frac{11}{8}x - \frac{3}{8} $
---
8. Standard form: $ 4x + 5y = 4 $
Solve for $ y $:
$$
5y = -4x + 4
$$
$$
y = -\frac{4}{5}x + \frac{4}{5}
$$
✔ Slope-intercept form: $ y = -\frac{4}{5}x + \frac{4}{5} $
---
9. Standard form: $ 10x - 12y = -4 $
Solve for $ y $:
$$
-12y = -10x - 4
$$
$$
y = \frac{10}{12}x + \frac{4}{12} = \frac{5}{6}x + \frac{1}{3}
$$
✔ Slope-intercept form: $ y = \frac{5}{6}x + \frac{1}{3} $
---
10. Standard form: $ 3x - y = 9 $
Solve for $ y $:
$$
-y = -3x + 9
$$
$$
y = 3x - 9
$$
✔ Slope-intercept form: $ y = 3x - 9 $
---
✔ Final Answers:
| Problem | Slope-Intercept Form |
|--------|------------------------|
| 1 | $ y = \frac{10}{7}x + \frac{8}{7} $ |
| 2 | $ y = -8x + 9 $ |
| 3 | $ y = -\frac{1}{6}x - \frac{1}{3} $ |
| 4 | $ y = -\frac{4}{3}x + 3 $ |
| 5 | $ y = -\frac{1}{4}x - \frac{2}{3} $ |
| 6 | $ y = -\frac{1}{2}x - 4 $ |
| 7 | $ y = \frac{11}{8}x - \frac{3}{8} $ |
| 8 | $ y = -\frac{4}{5}x + \frac{4}{5} $ |
| 9 | $ y = \frac{5}{6}x + \frac{1}{3} $ |
| 10 | $ y = 3x - 9 $ |
Let me know if you'd like these boxed or formatted differently!
Parent Tip: Review the logic above to help your child master the concept of linear equations slope intercept form worksheet.
