SOLUTION: Determine slope from a graph worksheet 2 - Studypool - Free Printable

You're working on a worksheet titled “Finding Slope From a Graph” from Kuta Software – Infinite Algebra 1. The goal is to find the slope of each line shown in the graphs.

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## 📌 What is Slope?

Slope measures the steepness of a line and is calculated as:

> Slope (m) = rise / run = (change in y) / (change in x) = (y₂ - y₁) / (x₂ - x₁)

You can pick any two points on the line, then count how many units you move up/down (rise) and left/right (run) to get from one point to the other.

- If the line goes uphill from left to right → positive slope
- If the line goes downhill from left to right → negative slope
- Horizontal line → slope = 0
- Vertical line → undefined slope

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Let’s solve each problem step-by-step.

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🔹 Problem 1:

Graph: Line passes through origin (0,0) and point (2,1)

- Pick two points: (0, 0) and (2, 1)
- Rise = 1 - 0 = +1
- Run = 2 - 0 = +2
- Slope = 1/2

✔ Answer: 1/2

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🔹 Problem 2:

Graph: Line passes through (-2, 1) and (0, -1) — or similar points

Let’s pick: (-2, 1) and (2, -3) — check grid carefully.

Actually, let's use: (0, -1) and (-2, 1)

- Rise = 1 - (-1) = +2
- Run = -2 - 0 = -2
- Slope = 2 / (-2) = -1

✔ Answer: -1

*(Alternatively, from (0,-1) to (2,-3): rise = -2, run = +2 → slope = -1)*

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🔹 Problem 3:

Graph: Line passes through (-2, -1) and (0, 0), or (2,1)

Pick: (0, 0) and (2, 1)

- Rise = 1 - 0 = +1
- Run = 2 - 0 = +2
- Slope = 1/2

✔ Answer: 1/2

*(Same as #1 — different position but same slope)*

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🔹 Problem 4:

Graph: Line passes through (0,0) and (-2, 2) or (2, -2)

Pick: (0, 0) and (2, -2)

- Rise = -2 - 0 = -2
- Run = 2 - 0 = +2
- Slope = -2/2 = -1

✔ Answer: -1

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🔹 Problem 5:

Graph: Horizontal line — parallel to x-axis

No matter which two points you pick, the y-values are the same, so:

- Rise = 0
- Run = any number ≠ 0
- Slope = 0 / run = 0

✔ Answer: 0

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🔹 Problem 6:

Graph: Vertical line — parallel to y-axis

Any two points have the same x-value, so:

- Run = 0
- Rise = any number ≠ 0
- Slope = rise / 0 → undefined

✔ Answer: undefined

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## ✔ Final Answers:

1) 1/2
2) -1
3) 1/2
4) -1
5) 0
6) undefined

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## 💡 Tip for Future Problems:

Always pick two clear points on the line (preferably where the line crosses grid intersections). Count rise over run — vertical change over horizontal change — and simplify the fraction if needed.

Let me know if you’d like to see how to write this on the worksheet or need help with more problems!