Graphing Linear Equations Worksheets with Answer Key - Free Printable

Let’s solve each problem one by one. We’ll sketch the graph for each equation or inequality step by step.

---

Problem 1: y > -x - 5

This is a linear inequality.

Step 1: Graph the line y = -x - 5 (as if it were an equation).
- Slope = -1, y-intercept = -5 → start at (0, -5)
- From there, go down 1, right 1 → point (1, -6)
- Or up 1, left 1 → point (-1, -4)

Step 2: Since it’s “>” (greater than), we use a dashed line (not solid) because the points on the line are NOT included.

Step 3: Shade the region above the line — because y is greater than the expression.

✔ Final graph: Dashed line with slope -1 through (0,-5), shaded above.

---

Problem 2: y = -3x - 3

This is a linear equation.

Step 1: Identify slope and y-intercept.
- Slope = -3, y-intercept = -3 → start at (0, -3)
- From (0, -3), go down 3, right 1 → (1, -6)
- Or up 3, left 1 → (-1, 0)

Step 2: Draw a solid line through these points.

✔ Final graph: Solid line passing through (0, -3) and (-1, 0).

---

Problem 3: x < -5

This is a vertical line inequality.

Step 1: The boundary is x = -5 → vertical line at x = -5.

Step 2: Since it’s “<”, use a dashed line (points on the line not included).

Step 3: Shade to the left of the line (where x values are less than -5).

✔ Final graph: Dashed vertical line at x = -5, shaded left.

---

Problem 4: x - 4y = 0

Rewrite in slope-intercept form to make graphing easier.

x - 4y = 0
→ -4y = -x
→ y = (1/4)x

Slope = 1/4, y-intercept = 0 → passes through origin (0,0)

From (0,0), go up 1, right 4 → (4,1)
Or down 1, left 4 → (-4,-1)

Draw a solid line through these points.

✔ Final graph: Solid line through (0,0) and (4,1).

---

Problem 5: 5x - 3y ≤ -15

First, rewrite in slope-intercept form.

5x - 3y ≤ -15
→ -3y ≤ -5x -15
→ Divide by -3 (remember to flip inequality sign!)
→ y ≥ (5/3)x + 5

Now graph:

Step 1: Line y = (5/3)x + 5
- y-intercept = 5 → (0,5)
- Slope = 5/3 → from (0,5), go up 5, right 3 → (3,10) — but that’s off grid? Let’s pick another point.
Try x = -3: y = (5/3)(-3) + 5 = -5 + 5 = 0 → (-3, 0)

So two points: (0,5) and (-3,0)

Step 2: Since it’s “≥”, use a solid line.

Step 3: Shade above the line (because y is greater than or equal).

✔ Final graph: Solid line through (0,5) and (-3,0), shaded above.

---

Problem 6: y = 3x - 4

Linear equation.

Slope = 3, y-intercept = -4 → (0, -4)

From (0, -4), go up 3, right 1 → (1, -1)
Or down 3, left 1 → (-1, -7)

Draw a solid line through these points.

✔ Final graph: Solid line through (0, -4) and (1, -1).

---

Final Answer:

Each problem has been solved by identifying key features (slope, intercept, inequality type), drawing the correct line (solid or dashed), and shading appropriately for inequalities. Graphs should reflect:

1. Dashed line y = -x - 5, shaded above
2. Solid line y = -3x - 3
3. Dashed vertical line x = -5, shaded left
4. Solid line y = (1/4)x
5. Solid line y = (5/3)x + 5, shaded above
6. Solid line y = 3x - 4