Graphing and writing linear equations in point-slope form worksheet.

Let’s solve each problem step by step.

We are working with point-slope form of a linear equation:
> y - y₁ = m(x - x₁)
This means the line passes through point (x₁, y₁) and has slope m.

But in these problems, the equations are written as:
- y = something + m(x - h) → which is actually slope-intercept form modified to show point-slope info
Actually, looking closely:

The given equations are in the form:
> y = b + m(x - h)
Which can be rewritten as:
> y - b = m(x - h) ← This IS point-slope form!

So for an equation like:
y = -2 + (1/3)(x + 3)
→ Rewrite as: y - (-2) = (1/3)(x - (-3))
→ So point is (-3, -2), slope is 1/3

Wait — let’s double-check that.

Actually, standard point-slope is:
y - y₁ = m(x - x₁)

If we have:
y = -2 + (1/3)(x + 3)
Then subtract -2 from both sides? No — better to rearrange:

Start with:
y = -2 + (1/3)(x + 3)
Add 2 to both sides:
y + 2 = (1/3)(x + 3)
Now write as:
y - (-2) = (1/3)(x - (-3))

✔ So yes — point is (-3, -2), slope is 1/3

Same logic applies to all.

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Problem 1:

Graph y = -2 + (1/3)(x + 3)

Rewrite:
y + 2 = (1/3)(x + 3)
→ y - (-2) = (1/3)(x - (-3))

So:
Point: (-3, -2)
Slope: 1/3

To graph:
- Plot point (-3, -2)
- From there, go up 1, right 3 (since slope = rise/run = 1/3)
- Draw line through those points

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Problem 2:

Graph y = 5 + 4(x + 2)

Rewrite:
y - 5 = 4(x + 2)
→ y - 5 = 4(x - (-2))

So:
Point: (-2, 5)
Slope: 4 (which is 4/1)

To graph:
- Plot (-2, 5)
- Go up 4, right 1
- Draw line

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Problem 3:

Graph y = 4 + -2(x - 3)

That’s: y = 4 - 2(x - 3)

Rewrite:
y - 4 = -2(x - 3)

So:
Point: (3, 4)
Slope: -2 (or -2/1)

To graph:
- Plot (3, 4)
- Go down 2, right 1 (because negative slope)
- Draw line

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Problem 4:

Graph y = -1 + (1/2)(x + 6)

Rewrite:
y + 1 = (1/2)(x + 6)
→ y - (-1) = (1/2)(x - (-6))

So:
Point: (-6, -1)
Slope: 1/2

To graph:
- Plot (-6, -1)
- Go up 1, right 2
- Draw line

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Let me verify each one again quickly:

1. y = -2 + (1/3)(x+3) → point (-3,-2), slope 1/3 ✔
2. y = 5 + 4(x+2) → point (-2,5), slope 4 ✔
3. y = 4 + -2(x-3) → point (3,4), slope -2 ✔
4. y = -1 + (1/2)(x+6) → point (-6,-1), slope 1/2 ✔

All correct.

Final Answer:

1. Point: (-3, -2), Slope: 1/3
2. Point: (-2, 5), Slope: 4
3. Point: (3, 4), Slope: -2
4. Point: (-6, -1), Slope: 1/2