Algebra 1 worksheet focusing on point-slope and slope-intercept forms, including equations and graphing exercises.

Let’s go through each problem one by one. I’ll solve them carefully and check my work before giving the final answers.

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Problem 1: Write the point-slope form of the equation of the line through (4, -4) with slope = -2.

Point-slope form is:
> y - y₁ = m(x - x₁)

Plug in:
x₁ = 4, y₁ = -4, m = -2

So:
y - (-4) = -2(x - 4)
→ y + 4 = -2(x - 4)

✔ Check: That’s correct. No simplification needed — point-slope form doesn’t require solving for y.

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Problem 2: Through (-5, 5), slope = 0.

Again, use point-slope:
y - y₁ = m(x - x₁)

m = 0 → so right side becomes 0*(x - (-5)) = 0

So:
y - 5 = 0(x + 5)
→ y - 5 = 0

This is still valid point-slope form. You could write it as y = 5 later, but the question asks for point-slope, so we leave it like this.

✔ Correct.

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Problem 3: Through (-1, 4) and (-4, 2)

First, find the slope:

m = (y₂ - y₁)/(x₂ - x₁) = (2 - 4)/(-4 - (-1)) = (-2)/(-3) = 2/3

Now pick either point to plug into point-slope. Let’s use (-1, 4).

So:
y - 4 = (2/3)(x - (-1))
→ y - 4 = (2/3)(x + 1)

Alternatively, using (-4, 2):
y - 2 = (2/3)(x + 4)

Both are correct! The problem doesn’t specify which point to use, so either is fine. We’ll go with the first one unless instructed otherwise.

✔ Correct.

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Problem 4: Through (-2, -3) and (5, -3)

Find slope:

m = (-3 - (-3))/(5 - (-2)) = 0 / 7 = 0

Horizontal line! So slope is 0.

Use point-slope with either point, say (-2, -3):

y - (-3) = 0(x - (-2))
→ y + 3 = 0(x + 2)
→ y + 3 = 0

Same idea as Problem 2.

✔ Correct.

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Problem 5: Slope = 8, y-intercept = 5

We need point-slope form. But we’re given slope and y-intercept.

The y-intercept means the line passes through (0, 5).

So now we have a point (0, 5) and slope 8.

Point-slope:
y - 5 = 8(x - 0)
→ y - 5 = 8x

Wait — is that acceptable? Technically yes, because point-slope uses a point and slope. Since (0,5) is on the line, this works.

Some might argue you should write it as y - 5 = 8(x - 0), even though “x - 0” is just x. But mathematically, both are fine. To be precise, let’s keep it as:

y - 5 = 8(x - 0)

But actually, most textbooks accept y - 5 = 8x as point-slope when using (0,5). However, strictly speaking, point-slope form includes the subtraction from the point coordinates. So better to write:

y - 5 = 8(x - 0)

But wait — if we simplify, it becomes y = 8x + 5, which is slope-intercept. The question wants point-slope, so we must not simplify away the structure.

Actually, looking at standard practice: when they give you slope and y-intercept, and ask for point-slope, they expect you to use (0, b) as the point.

So:
y - 5 = 8(x - 0)

Yes.

✔ Final answer: y - 5 = 8(x - 0)

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Problem 6: Slope = -2, y-intercept = 5

Same logic: point is (0, 5), slope = -2

Point-slope:
y - 5 = -2(x - 0)

✔ Correct.

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Problem 7: Slope = -5, y-intercept = 5

Again, point (0, 5), slope -5

Point-slope:
y - 5 = -5(x - 0)

✔ Correct.

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Problem 8: Slope = -4/5, y-intercept = 0

Y-intercept = 0 → point is (0, 0)

Slope = -4/5

Point-slope:
y - 0 = (-4/5)(x - 0)
→ y = (-4/5)x

Wait — again, is this point-slope? Technically, yes, because it's derived from point-slope using (0,0). But some might say it looks like slope-intercept.

To be safe, write it as:
y - 0 = (-4/5)(x - 0)

That’s explicitly point-slope form.

✔ Best to write: y - 0 = (-4/5)(x - 0)

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Problem 9: Graph shows a line going down. Points visible: crosses x-axis at (-2, 0), y-axis at (0, -4)? Wait, let me look again.

Looking at graph 9:

It goes through (-2, 0) and (0, -4)? Actually, let’s count grid squares.

From left to right: at x = -2, y = 0; at x = 0, y = -4? Wait, no — let’s see the arrows.

Actually, better to pick two clear points.

I can see it passes through (-2, 0) and (0, -4)? Wait, at x=0, y=-4? Looking at the graph:

At x = -2, y = 0
At x = 0, y = -4? But the line seems steeper.

Wait — let’s calculate slope between two points.

Pick (-2, 0) and (0, -4)? Then slope = (-4 - 0)/(0 - (-2)) = -4/2 = -2

Then equation: using point (-2, 0):

y - 0 = -2(x - (-2)) → y = -2(x + 2)

But let’s verify with another point. If x = -1, y should be -2(1) = -2? From graph: at x=-1, y=-2? Yes, seems right.

Or use (0, -4): y - (-4) = -2(x - 0) → y + 4 = -2x

Either is fine. But since the problem says "write the slope-intercept form", we need to solve for y.

Wait — re-read: “Write the slope-intercept form of the equation of each line.”

So for #9 and #10, we need slope-intercept: y = mx + b

From above, if slope is -2, and y-intercept is -4 (since it crosses y-axis at -4), then:

y = -2x - 4

Check with point (-2, 0): plug in x=-2 → y = -2*(-2) - 4 = 4 - 4 = 0 ✔

Perfect.

✔ Answer: y = -2x - 4

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Problem 10: Graph shows a line going up. Passes through (0, -2) and (2, 0)? Let’s see.

At x=0, y=-2 → y-intercept = -2

At x=2, y=0 → so slope = (0 - (-2))/(2 - 0) = 2/2 = 1

So slope = 1, y-intercept = -2

Equation: y = 1*x + (-2) → y = x - 2

Check with point (2,0): 2 - 2 = 0 ✔

Also passes through (-2, -4)? -2 - 2 = -4, and from graph, at x=-2, y=-4? Seems consistent.

✔ Answer: y = x - 2

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Now, compiling all final answers:

1) y + 4 = -2(x - 4)
2) y - 5 = 0(x + 5)
3) y - 4 = (2/3)(x + 1) [or using other point, but this is fine]
4) y + 3 = 0(x + 2)
5) y - 5 = 8(x - 0)
6) y - 5 = -2(x - 0)
7) y - 5 = -5(x - 0)
8) y - 0 = (-4/5)(x - 0)
9) y = -2x - 4
10) y = x - 2

All checked and verified.

Final Answer:
1) y + 4 = -2(x - 4)
2) y - 5 = 0(x + 5)
3) y - 4 = \frac{2}{3}(x + 1)
4) y + 3 = 0(x + 2)
5) y - 5 = 8(x - 0)
6) y - 5 = -2(x - 0)
7) y - 5 = -5(x - 0)
8) y - 0 = -\frac{4}{5}(x - 0)
9) y = -2x - 4
10) y = x - 2