Practice worksheet for determining slope, y-intercept, and linear equations from tables.

Let’s solve each table step by step. We’ll find the slope, then use it to find the y-intercept, and finally write the equation in slope-intercept form:
> y = mx + b
where *m* is slope, *b* is y-intercept.

---

🔹 Table #1

Points: (0, 4), (1, 6), (2, 8), (3, 10)

Step 1: Find slope (m)
Use two points — let’s pick (0, 4) and (1, 6).
Slope = (change in y) / (change in x) = (6 - 4) / (1 - 0) = 2 / 1 = 2

Check with another pair: (2, 8) and (3, 10) → (10-8)/(3-2) = 2/1 = 2 ✔

Step 2: Find y-intercept (b)
When x = 0, y = 4 → so b = 4

Equation: y = 2x + 4

✔ Matches answer key: “1. y = 2x + 4”

---

🔹 Table #2

Points: (-2, 6), (-1, 5), (0, 4), (1, 3)

Step 1: Slope
Pick (0, 4) and (1, 3):
(3 - 4) / (1 - 0) = -1 / 1 = -1

Check with (-1, 5) and (0, 4): (4 - 5)/(0 - (-1)) = (-1)/1 = -1 ✔

Step 2: y-intercept
At x=0, y=4 → b = 4

Equation: y = -1x + 4 → or y = -x + 4

✔ Matches answer key: “2. y = -x + 4”

---

🔹 Table #3

Points: (-2, 7), (-1, 9), (0, 11), (1, 13), (2, 15), (3, 17)

Step 1: Slope
Pick (0, 11) and (1, 13): (13 - 11)/(1 - 0) = 2/1 = 2

Check with (-1, 9) and (0, 11): (11 - 9)/(0 - (-1)) = 2/1 = 2 ✔

Step 2: y-intercept
At x=0, y=11 → b = 11

Equation: y = 2x + 11

✔ Matches answer key: “3. y = 2x + 11”

---

🔹 Table #4

Points: (-1, 7), (0, 22), (1, 37), (2, 52)

Wait — let’s check if this is linear.

From x=-1 to x=0: y goes from 7 to 22 → change = +15
From x=0 to x=1: y goes from 22 to 37 → change = +15
From x=1 to x=2: y goes from 37 to 52 → change = +15

So yes, constant rate → slope = 15 per 1 unit x → m = 15

y-intercept: at x=0, y=22 → b = 22

Equation: y = 15x + 22

But wait — look at the answer key:
“4. y = 15x + 22” → YES! It’s there.

✔ Correct.

---

🔹 Table #5

Points: (0, 7), (1, 10), (2, 13), (3, 16)

Step 1: Slope
(10 - 7)/(1 - 0) = 3/1 = 3

Check: (13 - 10)/(2 - 1) = 3/1 = 3 ✔

Step 2: y-intercept
At x=0, y=7 → b = 7

Equation: y = 3x + 7

✔ Matches answer key: “5. y = 3x + 7”

---

🔹 Table #6

Points: (-1, 2), (0, 5), (1, 8), (2, 11)

Step 1: Slope
(5 - 2)/(0 - (-1)) = 3/1 = 3

Or (8 - 5)/(1 - 0) = 3/1 = 3 ✔

Step 2: y-intercept
At x=0, y=5 → b = 5

Equation: y = 3x + 5

✔ Matches answer key: “6. y = 3x + 5”

---

All tables solved correctly. Let’s now compile final answers as requested.

Final Answer:
Table #1: Slope = 2, y-intercept = 4, Equation: y = 2x + 4
Table #2: Slope = -1, y-intercept = 4, Equation: y = -x + 4
Table #3: Slope = 2, y-intercept = 11, Equation: y = 2x + 11
Table #4: Slope = 15, y-intercept = 22, Equation: y = 15x + 22
Table #5: Slope = 3, y-intercept = 7, Equation: y = 3x + 7
Table #6: Slope = 3, y-intercept = 5, Equation: y = 3x + 5