Let's solve each of the given equations and rewrite them in
slope-intercept form, which is:
$$
y = mx + b
$$
where:
- $ m $ is the slope,
- $ b $ is the y-intercept.
We'll go through each equation step by step.
---
1) $ x + y = -15 $
Step 1: Solve for $ y $.
$$
x + y = -15
$$
Subtract $ x $ from both sides:
$$
y = -x - 15
$$
✔ Answer: $ y = -x - 15 $
---
2) $ 2y + 8x = 1 $
Step 1: Isolate $ y $.
$$
2y + 8x = 1
$$
Subtract $ 8x $ from both sides:
$$
2y = -8x + 1
$$
Divide every term by 2:
$$
y = -4x + \frac{1}{2}
$$
✔ Answer: $ y = -4x + \frac{1}{2} $
---
3) $ -2x + y = 1 $
Step 1: Solve for $ y $.
$$
-2x + y = 1
$$
Add $ 2x $ to both sides:
$$
y = 2x + 1
$$
✔ Answer: $ y = 2x + 1 $
---
4) $ 3y - 2x = 9 $
Step 1: Isolate $ y $.
$$
3y - 2x = 9
$$
Add $ 2x $ to both sides:
$$
3y = 2x + 9
$$
Divide every term by 3:
$$
y = \frac{2}{3}x + 3
$$
✔ Answer: $ y = \frac{2}{3}x + 3 $
---
5) $ 2y = -1x - 8 $
This one is almost in slope-intercept form. Just divide both sides by 2:
$$
y = -\frac{1}{2}x - 4
$$
✔ Answer: $ y = -\frac{1}{2}x - 4 $
---
6) $ y - 4 = -3(x - 3) $
This is in
point-slope form. Let's expand and simplify to slope-intercept form.
Start with:
$$
y - 4 = -3(x - 3)
$$
Distribute the $-3$:
$$
y - 4 = -3x + 9
$$
Add 4 to both sides:
$$
y = -3x + 13
$$
✔ Answer: $ y = -3x + 13 $
---
✔ Final Answers:
1) $ y = -x - 15 $
2) $ y = -4x + \frac{1}{2} $
3) $ y = 2x + 1 $
4) $ y = \frac{2}{3}x + 3 $
5) $ y = -\frac{1}{2}x - 4 $
6) $ y = -3x + 13 $
---
🔍 Summary:
To convert any linear equation into
slope-intercept form ($ y = mx + b $), follow these steps:
1. Isolate $ y $ on one side.
2. Simplify all terms (combine like terms, divide coefficients).
3. Ensure the equation is in the form $ y = mx + b $.
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 rewriting equations in slope intercept form worksheet.
