Sure! Let’s solve each problem step by step, rewriting equations into
slope-intercept form:
y = mx + b, where *m* is the slope and *b* is the y-intercept.
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## 🔢 PART 1: Rewrite equations in y = mx + b form
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① 2y = -1x - 6
We want to isolate y.
✔ Step 1: Divide both sides by 2:
> y = (-1/2)x - 6/2
>
y = -½x - 3
✔ Final Answer:
y = -½x - 3
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② y - 4x = 8
Isolate y by adding 4x to both sides.
✔ Step 1: Add 4x to both sides:
> y = 4x + 8
✔ Final Answer:
y = 4x + 8
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③ 0.8x + 0.4y = 1.2
Isolate y.
✔ Step 1: Subtract 0.8x from both sides:
> 0.4y = -0.8x + 1.2
✔ Step 2: Divide every term by 0.4:
> y = (-0.8 / 0.4)x + (1.2 / 0.4)
> y = -2x + 3
✔ Final Answer:
y = -2x + 3
*(Note: You can also multiply entire equation by 10 first to eliminate decimals: 8x + 4y = 12 → 4y = -8x + 12 → y = -2x + 3)*
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④ x + 6y = 4
Isolate y.
✔ Step 1: Subtract x from both sides:
> 6y = -x + 4
✔ Step 2: Divide by 6:
> y = (-1/6)x + 4/6
> y = -⅙x + ⅔
✔ Final Answer:
y = -⅙x + ⅔
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⑤ -x - y = -2
Isolate y.
✔ Step 1: Add x to both sides:
> -y = x - 2
✔ Step 2: Multiply both sides by -1:
> y = -x + 2
✔ Final Answer:
y = -x + 2
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⑥ y - 1 = (2/3)(x + 3)
This is in point-slope form. We need to distribute and simplify.
✔ Step 1: Distribute (2/3) on the right:
> y - 1 = (2/3)x + (2/3)(3)
> y - 1 = (2/3)x + 2
✔ Step 2: Add 1 to both sides:
> y = (2/3)x + 3
✔ Final Answer:
y = (2/3)x + 3
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## 📈 PART 2: Write equations given slope and point → use point-slope form → convert to slope-intercept
Use formula:
y - y₁ = m(x - x₁)
Then solve for y.
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⑦ Slope = -4/7, through (14, 3)
✔ Step 1: Plug into point-slope form:
> y - 3 = (-4/7)(x - 14)
✔ Step 2: Distribute -4/7:
> y - 3 = (-4/7)x + (4/7)(14)
> y - 3 = (-4/7)x + 8
✔ Step 3: Add 3 to both sides:
> y = (-4/7)x + 11
✔ Final Answer:
y = -⁴⁄₇x + 11
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⑧ Slope = 3, through (-5, 6)
✔ Step 1: Point-slope form:
> y - 6 = 3(x - (-5))
> y - 6 = 3(x + 5)
✔ Step 2: Distribute 3:
> y - 6 = 3x + 15
✔ Step 3: Add 6:
> y = 3x + 21
✔ Final Answer:
y = 3x + 21
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⑨ Slope = -4, through (-2, 5)
✔ Step 1: Point-slope:
> y - 5 = -4(x - (-2))
> y - 5 = -4(x + 2)
✔ Step 2: Distribute -4:
> y - 5 = -4x - 8
✔ Step 3: Add 5:
> y = -4x - 3
✔ Final Answer:
y = -4x - 3
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⑩ Slope = 5/3, through (3, 5)
✔ Step 1: Point-slope:
> y - 5 = (5/3)(x - 3)
✔ Step 2: Distribute 5/3:
> y - 5 = (5/3)x - 5
✔ Step 3: Add 5:
> y = (5/3)x
✔ Final Answer:
y = ⁵⁄₃x
*(Interesting — the y-intercept is 0! The line passes through origin.)*
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##
✔ FINAL ANSWERS SUMMARY:
Part 1:
1.
y = -½x - 3
2.
y = 4x + 8
3.
y = -2x + 3
4.
y = -⅙x + ⅔
5.
y = -x + 2
6.
y = (2/3)x + 3
Part 2:
7.
y = -⁴⁄₇x + 11
8.
y = 3x + 21
9.
y = -4x - 3
10.
y = ⁵⁄₃x
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Let me know if you’d like a graph or further explanation for any of these! 😊
Parent Tip: Review the logic above to help your child master the concept of slopes and intercepts worksheet answers.
