Graph - Match Linear Equations worksheet - Free Printable

Let’s solve each graph one by one. We’ll look at two things for each line:

1. Where it crosses the Y-axis (that’s the “+ b” part in y = mx + b)
2. How steep it is and which way it goes (that’s the “m” or slope)

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Graph 1:

- The line goes up as you move right → positive slope.
- It crosses the Y-axis at y = 2 → so the equation ends with “+ 2”.
- Let’s check the slope: from point (-2, -1) to (0, 2), we go up 3 and right 2? Wait — let’s pick easier points.

Actually, looking at red dots:
At x = -2, y = -1
At x = 0, y = 2
At x = 1, y = 3

From x=0 to x=1, y goes from 2 to 3 → that’s +1 over +1 → slope = 1.

So equation is: y = x + 2

✔ Matches first option.

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Graph 2:

- Line goes down as you move right → negative slope.
- Crosses Y-axis at y = 2 → so ends with “+ 2”
- Check slope: from (0,2) to (2,0): down 2, right 2 → slope = -1

Equation: y = -x + 2

✔ That’s the fourth option.

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Graph 3:

- Line goes down → negative slope.
- Crosses Y-axis at y = -2 → ends with “- 2”
- Check slope: from (0,-2) to (1,-4): down 2, right 1 → slope = -2

Equation: y = -2x - 2

✔ That’s the seventh option.

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Graph 4:

- Line goes up → positive slope.
- Crosses Y-axis at y = 2 → ends with “+ 2”
- Check slope: from (0,2) to (2,3): up 1, right 2 → slope = 1/2

Equation: y = (1/2)x + 2

✔ That’s the fifth option.

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Now, what about the other equations? They’re extras.

We used:
- y = x + 2 → Graph 1
- y = -x + 2 → Graph 2
- y = -2x - 2 → Graph 3
- y = (1/2)x + 2 → Graph 4

Leftover equations:
- y = x - 2
- y = -x - 2
- y = (1/2)x - 2
- y = -2x + 2

These are the “Extra” answers.

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Final Answer:

1. y = x + 2
2. y = -x + 2
3. y = -2x - 2
4. y = (1/2)x + 2

Extra = y = x - 2
Extra = y = -x - 2
Extra = y = (1/2)x - 2
Extra = y = -2x + 2