Worksheet for writing slope-intercept form equations from scatter plot trend lines.

To find the equation of the trend line for each scatter plot, we use the slope-intercept form:

y = mx + b

Where:
- m is the slope (rise over run)
- b is the y-intercept (where the line crosses the y-axis)

We’ll go through each graph one by one. Since these are hand-drawn trend lines on grid paper, we estimate two clear points on each line to calculate slope and intercept.

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Graph ①

Line goes from top-left to bottom-right → negative slope.

Pick two points:
Approximately (0, 8) and (10, 4)

Slope m = (4 - 8)/(10 - 0) = (-4)/10 = -0.4

Y-intercept b = 8 (since it crosses y-axis at 8)

→ Equation: y = -0.4x + 8

*(Check with another point: at x=5, y should be -0.4*5 + 8 = -2 + 8 = 6 — looks correct on graph)*

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Graph ②

Line goes up to the right → positive slope.

Points: approx (0, 2) and (10, 7)

m = (7 - 2)/(10 - 0) = 5/10 = 0.5

b = 2

→ Equation: y = 0.5x + 2

*(Check: x=4 → y=0.5*4+2=4 — matches graph)*

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Graph ③

Positive slope.

Points: (0, 1) and (10, 6)

m = (6 - 1)/10 = 5/10 = 0.5

b = 1

→ Equation: y = 0.5x + 1

*(Check: x=6 → y=0.5*6+1=4 — looks good)*

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Graph ④

Negative slope.

Points: (0, 6) and (10, 3)

m = (3 - 6)/10 = -3/10 = -0.3

b = 6

→ Equation: y = -0.3x + 6

*(Check: x=5 → y=-1.5+6=4.5 — reasonable)*

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Graph

Negative slope.

Points: (0, 9) and (10, 4)

m = (4 - 9)/10 = -5/10 = -0.5

b = 9

→ Equation: y = -0.5x + 9

*(Check: x=4 → y=-2+9=7 — matches)*

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Graph ⑥

Negative slope.

Points: (0, 8) and (8, 0) — wait, let’s pick easier ones.

Actually, looks like it passes through (0, 8) and (10, 3)

m = (3 - 8)/10 = -5/10 = -0.5

b = 8

→ Equation: y = -0.5x + 8

*(Check: x=4 → y=-2+8=6 — yes)*

Wait — actually looking again, maybe better points: (2,7) and (8,4)? Let's recalculate.

From (0,8) to (10,3): same as above → still -0.5x + 8.

But let me check if it hits (5, 5.5)? -0.5*5 + 8 = -2.5 + 8 = 5.5 — yes.

So okay.

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Graph

This one is tricky — the line is almost flat but slightly increasing? Wait — no, looking closely, it seems horizontal? But there’s a slight upward tilt.

Actually, looking at the dots and line: starts near (0, 2), ends near (10, 3)

So very shallow positive slope.

Points: (0, 2) and (10, 3)

m = (3 - 2)/10 = 1/10 = 0.1

b = 2

→ Equation: y = 0.1x + 2

*(Check: x=5 → y=0.5+2=2.5 — looks about right)*

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Graph ⑧

Negative slope.

Points: (0, 7) and (10, 3)

m = (3 - 7)/10 = -4/10 = -0.4

b = 7

→ Equation: y = -0.4x + 7

*(Check: x=5 → y=-2+7=5 — matches)*

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Graph ⑨

Positive slope.

Points: (0, 1) and (5, 6) — or (10, 11)? Too high.

Better: (0, 1) and (5, 6)

m = (6 - 1)/5 = 5/5 = 1

b = 1

→ Equation: y = 1x + 1 or just y = x + 1

*(Check: x=3 → y=4 — looks correct on graph)*

Wait — does it pass through (0,1)? Yes. At x=4, y=5? On graph, yes.

Perfect.

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Now, compiling all answers:

Final Answer:

① y = -0.4x + 8
② y = 0.5x + 2
③ y = 0.5x + 1
④ y = -0.3x + 6
⑤ y = -0.5x + 9
⑥ y = -0.5x + 8
⑦ y = 0.1x + 2
⑧ y = -0.4x + 7
⑨ y = x + 1