Algebra I Slope Intercept Form Worksheet 1 featuring questions on slope intercept form, equations to convert to slope-intercept form, and graphs to plot with slope and y-intercept.

Let’s go step by step to solve each part of the worksheet.

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Part 1: What is slope intercept form?

Slope intercept form is a way to write the equation of a straight line. It looks like this:

> y = mx + b

This form tells you two important things about the line:
- How steep it is (the slope)
- Where it crosses the y-axis (the y-intercept)

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Part 2: What does the m represent?

In the equation y = mx + b, m represents the slope of the line.

Slope tells you how much y changes for every 1 unit change in x.
For example, if m = 2, then for every 1 step right on the x-axis, the line goes up 2 steps on the y-axis.

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Part 3: What does the b represent?

In the equation y = mx + b, b represents the y-intercept.

That’s the point where the line crosses the y-axis — when x = 0.

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Part 4: Put each equation into slope intercept form.

We need to rearrange each equation so it looks like y = mx + b.

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Problem 1: y - 3x = 19

Add 3x to both sides:

→ y = 3x + 19 ✔

Already in slope intercept form.

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Problem 2: 2y - 8x = 20

First, add 8x to both sides:

→ 2y = 8x + 20

Now divide everything by 2:

→ y = 4x + 10 ✔

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Problem 3: 15 = -3y + 21x

We want y alone on one side.

Subtract 21x from both sides:

→ 15 - 21x = -3y

Or better: rewrite as:

→ -3y = -21x + 15

Now divide everything by -3:

→ y = (-21/-3)x + 15/(-3)

→ y = 7x - 5 ✔

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Problem 4: 5x - 6y = 22

Subtract 5x from both sides:

→ -6y = -5x + 22

Divide everything by -6:

→ y = (-5/-6)x + 22/(-6)

→ y = (5/6)x - 22/6

Simplify 22/6 → divide numerator and denominator by 2 → 11/3

So:

→ y = (5/6)x - 11/3 ✔

(Note: The problem says “leave any fractions as simplified improper fractions” — but 11/3 is already simplified and improper, so that’s fine.)

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Problem 5: -y = -7x + 32

Multiply both sides by -1 to make y positive:

→ y = 7x - 32 ✔

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Problem 6: 7y + 42 = -14x

Subtract 42 from both sides:

→ 7y = -14x - 42

Divide everything by 7:

→ y = (-14/7)x - 42/7

→ y = -2x - 6 ✔

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Part 5: Graph each equation. State the slope and y-intercept.

We don’t need to graph here since we’re just solving textually, but we can state slope and y-int.

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Graph Problem 1: y = 2x + 5

This is already in slope intercept form.

→ Slope (m) = 2
→ y-intercept (b) = 5

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Graph Problem 2: -y = (2/3)x + 4

We need to solve for y first.

Multiply both sides by -1:

→ y = -(2/3)x - 4

Now it’s in slope intercept form.

→ Slope (m) = -2/3
→ y-intercept (b) = -4

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✔ All problems solved and verified.

Final Answer:
What is slope intercept form? y = mx + b
What does the m represent: slope
What does the b represent: y-intercept

1. y = 3x + 19
2. y = 4x + 10
3. y = 7x - 5
4. y = (5/6)x - 11/3
5. y = 7x - 32
6. y = -2x - 6

Graph 1: Slope: 2, y-int: 5
Graph 2: Slope: -2/3, y-int: -4