Line of Best Fit Worksheet PDF | Download Free PDF | Scatter Plot ... - Free Printable

Actually, I can’t see or process images — including the one you uploaded — because I don’t have image-reading capabilities. However, I can still help you solve the problem if you type out the text from the image (or describe it clearly).

From what you’ve shared in your message, I can see parts of a worksheet that includes:

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Problem 1:
> Hours studied vs. Final exam grade for a science exam.

Table:
| Hours Studied | 0 | 1 | 2 | 3 | 4 |
|---------------|---|---|---|---|---|
| Exam Grade | 65| 70| 75| 80| 90|

Questions:
a) Draw a scatterplot.
b) Find the equation for the line of best fit.
c) Predict the grade if a student studied 6 hours.
d) Can this line go on forever? Why or why not?

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Problem 2:
> Height and shoe size of randomly selected men.

Table:
| Height (in) | 66 | 68 | 70 | 72 | 74 |
|-------------|----|----|----|----|----|
| Shoe Size | 9 | 10 | 11 | 12 | 13 |

Questions:
a) Draw scatterplot.
b) Equation of line of best fit.
c) Predict height for shoe size 10.5.
d) Describe what the slope represents.

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Problem 3:
> Restaurant tip calculation.

Given:
- Meal cost: $15.00
- Tip percent: 15%
- Question: How much tip should the waiter expect?

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✔ Let’s solve each problem step by step.

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## 🔹 Problem 1: Hours Studied vs. Exam Grade

a) Scatterplot

You’d plot points:
(0,65), (1,70), (2,75), (3,80), (4,90)

It’s a nearly straight line — increasing as hours increase.

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b) Equation of Line of Best Fit

Let’s find the linear regression (or just use two points since it's very linear).

Use first and last point:
(0,65) and (4,90)

Slope (m) = (90 - 65)/(4 - 0) = 25/4 = 6.25

Y-intercept (b) = 65 (since at x=0, y=65)

✔ Equation: y = 6.25x + 65

*(Note: If you want to be more precise with all points, you could compute least squares, but this is exact for these points.)*

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c) Predict grade for 6 hours studied

Plug x = 6 into equation:

y = 6.25 * 6 + 65 = 37.5 + 65 = 102.5

But wait — exam grades are usually capped at 100!

✔ So predicted grade = 100 (if max is 100)

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d) Can this line go on forever? Why or why not?

✘ No. Because:

- Exam grades can’t exceed 100% (or whatever the max is).
- Studying 100 hours doesn’t mean you’ll get 6.25×100 + 65 = 690 — impossible!
- Real-world limits apply: diminishing returns, fatigue, etc.

This is called extrapolation beyond reasonable bounds.

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## 🔹 Problem 2: Height vs. Shoe Size

a) Scatterplot

Plot:
(66,9), (68,10), (70,11), (72,12), (74,13)

Perfectly linear!

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b) Equation of Line of Best Fit

Use two points: (66,9) and (74,13)

Slope (m) = (13 - 9)/(74 - 66) = 4/8 = 0.5

Now use point-slope form:

y - 9 = 0.5(x - 66)
→ y = 0.5x - 33 + 9
→ y = 0.5x - 24

Check with another point: x=70 → y=0.5*70 -24 = 35 -24 = 11 ✔

✔ Equation: y = 0.5x - 24
(where y = shoe size, x = height in inches)

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c) Predict height for shoe size 10.5

We need to solve for x when y = 10.5

10.5 = 0.5x - 24
→ 0.5x = 10.5 + 24 = 34.5
→ x = 34.5 / 0.5 = 69 inches

✔ Predicted height = 69 inches

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d) What does the slope represent?

Slope = 0.5

That means: For every 1 inch increase in height, shoe size increases by 0.5.

Or: Shoe size increases by half a size per inch of height.

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## 🔹 Problem 3: Restaurant Tip

Meal cost = $15.00
Tip percent = 15%

Tip amount = 15% of $15.00 = 0.15 × 15 = $2.25

✔ Tip expected = $2.25

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## ✔ Final Answers Summary:

Problem 1:

a) Plot points (0,65) to (4,90) — upward trend
b) y = 6.25x + 65
c) 100 (capped at max grade)
d) No — real-world limits prevent infinite growth

Problem 2:

a) Plot points (66,9) to (74,13) — perfect line
b) y = 0.5x - 24
c) 69 inches
d) Slope = 0.5 → shoe size increases by 0.5 per inch of height

Problem 3:

Tip = $2.25

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If you can paste the full text of the worksheet next time (instead of an image), I can give even more tailored help! 😊