Slope Intercept Form Worksheets with Answer Key - Free Printable

Let’s solve each problem step by step, explaining how to find x-intercepts and y-intercepts, and then how to sketch the graphs.

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## 🔍 What are x- and y-intercepts?

- x-intercept: The point where a line crosses the x-axis → y = 0
- y-intercept: The point where a line crosses the y-axis → x = 0

To find them:
- For x-intercept, set y = 0 in the equation and solve for x
- For y-intercept, set x = 0 in the equation and solve for y

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## ✔ Problem 1: `3x - y = 9`

➤ x-intercept (set y = 0):

```
3x - 0 = 9
→ 3x = 9
→ x = 3
✔ x-intercept: (3, 0)
```

➤ y-intercept (set x = 0):

```
3(0) - y = 9
→ -y = 9
→ y = -9
✔ y-intercept: (0, -9)
```

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## ✔ Problem 2: `2x + 3y = 6`

➤ x-intercept (set y = 0):

```
2x + 0 = 6
→ 2x = 6
→ x = 3
✔ x-intercept: (3, 0)
```

➤ y-intercept (set x = 0):

```
0 + 3y = 6
→ 3y = 6
→ y = 2
✔ y-intercept: (0, 2)
```

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## ✔ Problem 3: `x - 2y = -10`

➤ x-intercept (set y = 0):

```
x - 0 = -10
→ x = -10
✔ x-intercept: (-10, 0)
```

➤ y-intercept (set x = 0):

```
0 - 2y = -10
→ -2y = -10
→ y = 5
✔ y-intercept: (0, 5)
```

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## ✔ Problem 4: `7x + 5y = 42`

➤ x-intercept (set y = 0):

```
7x + 0 = 42
→ 7x = 42
→ x = 6
✔ x-intercept: (6, 0)
```

➤ y-intercept (set x = 0):

```
0 + 5y = 42
→ 5y = 42
→ y = 42/5 = 8.4
✔ y-intercept: (0, 8.4)
```

> *Note: You can write it as a fraction: 42/5 or decimal 8.4*

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## 📈 Problems 5 & 6: Sketch the graph using given intercepts

You don’t need an equation — just plot the two intercept points and draw a straight line through them!

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## ✔ Problem 5: x-intercept = 5, y-intercept = -4

- Plot point (5, 0) on the x-axis
- Plot point (0, -4) on the y-axis
- Draw a straight line connecting them.

👉 This line goes from bottom-left to top-right (positive slope).

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## ✔ Problem 6: x-intercept = -2, y-intercept = -3

- Plot point (-2, 0) on the x-axis
- Plot point (0, -3) on the y-axis
- Draw a straight line connecting them.

👉 This line also has a positive slope (since both intercepts are negative, the line rises from left to right).

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## 🧾 Final Answers:

1. `3x - y = 9`

- x-intercept: 3, y-intercept: -9

2. `2x + 3y = 6`

- x-intercept: 3, y-intercept: 2

3. `x - 2y = -10`

- x-intercept: -10, y-intercept: 5

4. `7x + 5y = 42`

- x-intercept: 6, y-intercept: 8.4 (or 42/5)

5. Graph: Line through (5, 0) and (0, -4)

6. Graph: Line through (-2, 0) and (0, -3)

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## 🖍️ How to Sketch (Quick Tips):

- On the grid, find the x-intercept → go along x-axis to that number, mark point.
- Find y-intercept → go up/down y-axis to that number, mark point.
- Use a ruler to connect the two points with a straight line.
- Extend the line slightly beyond the points to show it's infinite.

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✔ You’ve now solved all problems! Let me know if you’d like to see the actual graphs drawn or need help plotting them on paper.