Finding Slope From Tables Worksheet - Fill Online, Printable ... - Free Printable

Of course! I'll solve the problem for each of the 12 tables, calculate the slope (m), and describe the graph.

The formula for slope (m) is:
m = (change in y) / (change in x) = (y₂ - y₁) / (x₂ - x₁)

We can pick any two points from the table to calculate the slope. If the slope is constant between all pairs of points, then the data represents a straight line.

---

Problem 1

Table:
```
x | y
-2| 3
-1| 5
0| 7
1| 9
2|11
```

Slope Calculation:
Pick (-2, 3) and (0, 7):
m = (7 - 3) / (0 - (-2)) = 4 / 2 = 2

Check another pair: (0,7) and (2,11):
m = (11 - 7) / (2 - 0) = 4 / 2 = 2

✔ Slope is constant.

Graph Description: Increasing (since m > 0)

---

Problem 2

Table:
```
x | y
-3| 5
-2| 2
-1|-1
0|-4
1|-7
```

Slope Calculation:
Pick (-3, 5) and (0, -4):
m = (-4 - 5) / (0 - (-3)) = (-9) / 3 = -3

Check another pair: (-1,-1) and (1,-7):
m = (-7 - (-1)) / (1 - (-1)) = (-6)/2 = -3

✔ Slope is constant.

Graph Description: Decreasing (since m < 0)

---

Problem 3

Table:
```
x | y
1|-17
2|-13
3| -9
4| -5
5| -1
```

Slope Calculation:
Pick (1, -17) and (3, -9):
m = (-9 - (-17)) / (3 - 1) = (8)/2 = 4

Check (2,-13) and (5,-1):
m = (-1 - (-13)) / (5 - 2) = 12/3 = 4

✔ Slope is constant.

Graph Description: Increasing (since m > 0)

---

Problem 4

Table:
```
x | y
-6| -4
-5| -9
-4|-14
-3|-19
-2|-24
```

Slope Calculation:
Pick (-6, -4) and (-4, -14):
m = (-14 - (-4)) / (-4 - (-6)) = (-10)/2 = -5

Check (-5,-9) and (-2,-24):
m = (-24 - (-9)) / (-2 - (-5)) = (-15)/3 = -5

✔ Slope is constant.

Graph Description: Decreasing (since m < 0)

---

Problem 5

Table:
```
x | y
0| 3
1|5.5
2| 8
3|10.5
4| 13
```

Slope Calculation:
Pick (0,3) and (2,8):
m = (8 - 3) / (2 - 0) = 5/2 = 2.5

Check (1,5.5) and (4,13):
m = (13 - 5.5) / (4 - 1) = 7.5 / 3 = 2.5

✔ Slope is constant.

Graph Description: Increasing (since m > 0)

---

Problem 6

Table:
```
x | y
-2 | 5
-1 |4.75
0 | 4.5
1 |4.25
2 | 4
```

Slope Calculation:
Pick (-2,5) and (0,4.5):
m = (4.5 - 5) / (0 - (-2)) = (-0.5)/2 = -0.25

Check (1,4.25) and (2,4):
m = (4 - 4.25) / (2 - 1) = (-0.25)/1 = -0.25

✔ Slope is constant.

Graph Description: Decreasing (since m < 0)

---

Problem 7

Table:
```
x | y
-2 | 2/5
-1 | 4/5
0 | 6/5
1 | 8/5
```

Slope Calculation:
Pick (-2, 2/5) and (0, 6/5):
m = (6/5 - 2/5) / (0 - (-2)) = (4/5) / 2 = 4/10 = 2/5

Check (-1,4/5) and (1,8/5):
m = (8/5 - 4/5) / (1 - (-1)) = (4/5)/2 = 2/5

✔ Slope is constant.

Graph Description: Increasing (since m > 0)

---

Problem 8

Table:
```
x | y
-1| 1
1| 2
3| 3
5| 4
7| 5
```

Slope Calculation:
Pick (-1,1) and (3,3):
m = (3 - 1) / (3 - (-1)) = 2 / 4 = 0.5

Check (1,2) and (7,5):
m = (5 - 2) / (7 - 1) = 3 / 6 = 0.5

✔ Slope is constant.

Graph Description: Increasing (since m > 0)

---

Problem 9

Table:
```
x | y
-5|10
-2| 5
1| 0
4|-5
7|-10
```

Slope Calculation:
Pick (-5,10) and (1,0):
m = (0 - 10) / (1 - (-5)) = (-10)/6 = -5/3

Check (-2,5) and (4,-5):
m = (-5 - 5) / (4 - (-2)) = (-10)/6 = -5/3

✔ Slope is constant.

Graph Description: Decreasing (since m < 0)

---

Problem 10

Table:
```
x | y
-5|10
-3| 6
-1| 2
1|-2
3|-6
```

Slope Calculation:
Pick (-5,10) and (-1,2):
m = (2 - 10) / (-1 - (-5)) = (-8)/4 = -2

Check (1,-2) and (3,-6):
m = (-6 - (-2)) / (3 - 1) = (-4)/2 = -2

✔ Slope is constant.

Graph Description: Decreasing (since m < 0)

---

Problem 11

Table:
```
x | y
-4| 6
-2| 6
0| 6
2| 6
4| 6
```

Slope Calculation:
Pick (-4,6) and (2,6):
m = (6 - 6) / (2 - (-4)) = 0 / 6 = 0

All y-values are the same → horizontal line.

✔ Slope is constant (zero).

Graph Description: Horizontal (since m = 0)

---

Problem 12

Table:
```
x | y
5| 2
5| 4
5| 6
5| 8
5|10
```

Slope Calculation:
Pick (5,2) and (5,6):
m = (6 - 2) / (5 - 5) = 4 / 0 → Undefined

All x-values are the same → vertical line.

✔ Slope is undefined.

Graph Description: Vertical (since slope is undefined)

---

## ✔ Final Answers Summary:

| Problem | Slope (m) | Graph Description |
|---------|----------------|-------------------|
| 1 | 2 | Increasing |
| 2 | -3 | Decreasing |
| 3 | 4 | Increasing |
| 4 | -5 | Decreasing |
| 5 | 2.5 | Increasing |
| 6 | -0.25 | Decreasing |
| 7 | 2/5 | Increasing |
| 8 | 0.5 | Increasing |
| 9 | -5/3 | Decreasing |
| 10 | -2 | Decreasing |
| 11 | 0 | Horizontal |
| 12 | Undefined | Vertical |

---

💡 Bonus: Real-world situation example (for Problem 1)

> Situation for Table 1: A car travels at a constant speed. The table shows time (x, in hours) and distance traveled (y, in miles). At hour 0, it has traveled 7 miles; after 1 more hour, it has traveled 9 miles — so it’s moving at 2 miles per hour. The graph is increasing, showing the car is covering more distance over time.

You can copy this table and situation on the back of the page as instructed!

Let me know if you’d like help writing the situation for another table.