Graphing Linear Equations Worksheet - Algebra Accents - Free Printable

You've uploaded a worksheet titled “GRAPHING LINEAR EQUATIONS: Standard Form”, which contains 8 problems (numbered 9–16). Each problem asks you to:

1. Graph the given linear equation (in standard form: Ax + By = C),
2. Find the slope,
3. Find the y-intercept.

---

Let’s solve each one step by step, explaining how to find slope and y-intercept from standard form, and how to graph.

---

## 🔑 Key Concept: Standard Form → Slope-Intercept Form

Standard form:
> Ax + By = C

To find slope (m) and y-intercept (b), convert to slope-intercept form:
> y = mx + b

Steps:

1. Solve for y.
2. Coefficient of x → slope (m)
3. Constant term → y-intercept (b)

---

## 📊 Problem 9: `x - 5y = 10`

Step 1: Solve for y

```
x - 5y = 10
→ -5y = -x + 10
→ y = (1/5)x - 2
```

✔ Slope = 1/5
✔ Y-intercept = -2

Graphing tip: Plot (0, -2), then go up 1, right 5 to next point.

---

## 📊 Problem 10: `2x + y = -5`

Step 1: Solve for y

```
2x + y = -5
→ y = -2x - 5
```

✔ Slope = -2
✔ Y-intercept = -5

Graphing tip: Plot (0, -5), then down 2, right 1.

---

## 📊 Problem 11: `x = -10`

This is a vertical line.

⚠️ Slope is undefined (because vertical lines have no "run" — denominator zero)

✔ Y-intercept = none (never crosses y-axis unless x=0, which it’s not)

Graphing tip: Draw vertical line at x = -10.

---

## 📊 Problem 12: `x + 3y = -15`

Step 1: Solve for y

```
x + 3y = -15
→ 3y = -x -15
→ y = (-1/3)x - 5
```

✔ Slope = -1/3
✔ Y-intercept = -5

Graphing tip: Plot (0, -5), then down 1, right 3.

---

## 📊 Problem 13: `x - y = -5`

Step 1: Solve for y

```
x - y = -5
→ -y = -x -5
→ y = x + 5
```

✔ Slope = 1
✔ Y-intercept = 5

Graphing tip: Plot (0, 5), then up 1, right 1.

---

## 📊 Problem 14: `3x + 2y = -8`

Step 1: Solve for y

```
3x + 2y = -8
→ 2y = -3x -8
→ y = (-3/2)x - 4
```

✔ Slope = -3/2
✔ Y-intercept = -4

Graphing tip: Plot (0, -4), then down 3, right 2.

---

## 📊 Problem 15: `3x - 5y = -3`

Step 1: Solve for y

```
3x - 5y = -3
→ -5y = -3x -3
→ y = (3/5)x + 3/5
```

✔ Slope = 3/5
✔ Y-intercept = 3/5 (or 0.6)

Graphing tip: Plot (0, 0.6), then up 3, right 5.

---

## 📊 Problem 16: `7x + y = -8`

Step 1: Solve for y

```
7x + y = -8
→ y = -7x - 8
```

✔ Slope = -7
✔ Y-intercept = -8

Graphing tip: Plot (0, -8), then down 7, right 1.

---

## ✔ Final Answers Summary:

| Problem | Equation | Slope | Y-intercept |
|---------|------------------|-----------|-------------|
| 9 | x - 5y = 10 | 1/5 | -2 |
| 10 | 2x + y = -5 | -2 | -5 |
| 11 | x = -10 | Undefined | None |
| 12 | x + 3y = -15 | -1/3 | -5 |
| 13 | x - y = -5 | 1 | 5 |
| 14 | 3x + 2y = -8 | -3/2 | -4 |
| 15 | 3x - 5y = -3 | 3/5 | 3/5 |
| 16 | 7x + y = -8 | -7 | -8 |

---

## 🖍️ Graphing Tips Recap:

- Always start by plotting the y-intercept (0, b).
- Use slope = rise/run to find another point.
- For vertical lines (x = constant): draw straight up/down at that x-value.
- For horizontal lines (y = constant): draw left/right at that y-value (not here).

---

Let me know if you want printable answer keys or graphs drawn out! 😊