Let’s solve each table one by one to find the
slope and
y-intercept.
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🔢 What is slope?
Slope = how much y changes when x increases by 1.
We can calculate it using any two points:
>
Slope (m) = (change in y) / (change in x)
📍 What is y-intercept?
It’s the value of
y when x = 0. If a table has a row where x=0, that y-value is the y-intercept!
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##
✔ Table 1 (Top Left)
| x | y |
|---|---|
| 0 | 8 |
| 2 | 14 |
| 3 | 17 |
| 5 | 23 |
→ Since x=0 gives y=8 →
Y-intercept = 8
Now check slope between (0,8) and (2,14):
Change in y = 14 - 8 = 6
Change in x = 2 - 0 = 2
Slope = 6/2 =
3
Check another pair to confirm: (2,14) and (3,17)
Δy = 17-14 = 3, Δx = 3-2 = 1 → Slope = 3 ✔️
✔ Slope: 3, Y-intercept: 8
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##
✔ Table 2 (Top Right)
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y | 5 | 3 | 1 |-1 |-3 |
→ When x=0, y=5 →
Y-intercept = 5
Check slope from x=0 to x=1:
Δy = 3 - 5 = -2, Δx = 1 → Slope = -2
Check next: x=1 to x=2 → y goes 3→1 → Δy=-2, Δx=1 → Slope=-2 ✔️
✔ Slope: -2, Y-intercept: 5
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##
✔ Table 3 (Bottom Left)
| X | Y |
|----|----|
| -6 | -19|
| -3 | -22|
| 0 | -25|
| 3 | -28|
→ When x=0, y=-25 →
Y-intercept = -25
Check slope from x=0 to x=3:
Δy = -28 - (-25) = -3, Δx = 3 → Slope = -3/3 =
-1
Check another: x=-3 to x=0 → y: -22 to -25 → Δy = -3, Δx=3 → Slope=-1 ✔️
✔ Slope: -1, Y-intercept: -25
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##
✔ Table 4 (Bottom Right)
| x | y |
|----|----|
| -3 | -11|
| 0 | -8 |
| 2 | -6 |
| 4 | -4 |
| 7 | -1 |
→ When x=0, y=-8 →
Y-intercept = -8
Check slope from x=0 to x=2:
Δy = -6 - (-8) = 2, Δx = 2 → Slope = 2/2 =
1
Check x=2 to x=4: y from -6 to -4 → Δy=2, Δx=2 → Slope=1 ✔️
Check x=4 to x=7: y from -4 to -1 → Δy=3, Δx=3 → Slope=1 ✔️
✔ Slope: 1, Y-intercept: -8
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Final Answer:
Table 1: Slope: 3, Y-intercept: 8
Table 2: Slope: -2, Y-intercept: 5
Table 3: Slope: -1, Y-intercept: -25
Table 4: Slope: 1, Y-intercept: -8
Parent Tip: Review the logic above to help your child master the concept of finding slope and y intercept from a table worksheet.
