Worksheet on scatter plots and lines of best fit with problems related to music sales, family costs, data points, and education grades.

Let’s go through each problem one by one, carefully checking calculations and logic.

---

Problem 1: MUSIC – CDs sold from 1999 to 2005

We are given two points on the line of best fit:
- (810, 2002) → This means in year 2002, 810 million CDs were sold? Wait — that doesn’t make sense. Actually, looking at the graph and handwritten work, it seems the x-axis is years ('99 to '05), and y-axis is millions of CDs.

But the student wrote:
(810, 2002) and (740, 2003) — this must be a mix-up. Probably they meant:

In 2002 → 810 million? But the graph shows around 850–900 for 2002. Let’s re-express.

Actually, looking at the scatter plot description: “number of CDs (in millions) sold from 1999 to 2005”. The graph has x-axis labeled ‘99 to ‘05, and y-axis from 650 to 950 (millions).

The student calculated slope using:

From 2002 to 2003:
Change in y = 740 - 810 = -70
Change in x = 2003 - 2002 = 1
So slope m = -70 / 1 = -70

Wait — but then they wrote:
“y - 2002 = (-1/70)(x - 810)” — that’s backwards! They swapped x and y.

Actually, if we assume:
- x = year
- y = millions of CDs

Then point A: (2002, 810)
Point B: (2003, 740)

Slope m = (740 - 810)/(2003 - 2002) = (-70)/1 = -70

Equation: y - 810 = -70(x - 2002)

Now plug in x = 2006:

y = -70*(2006 - 2002) + 810
= -70*4 + 810
= -280 + 810
= 530

But wait — the student got y = (1/70)x + 2013.6 — which is wrong because they inverted slope and variables.

Also, visually, from 2005 (~700?) to 2006, continuing downward trend — 530 seems too low? Let’s check another pair.

Looking at graph: In 1999, ~950; in 2005, ~700. That’s over 6 years, drop of 250 → about 41.6 per year.

From 2005 to 2006: 700 - 41.6 ≈ 658.4

But student used only 2002–2003 data — maybe those are exact values from table not shown? Since worksheet says “scatter plot shows”, perhaps we should use their given points.

Student used (810,2002) and (740,2003) — treating CD sales as x and year as y? That would be unusual.

Actually, rereading: “If the trend continued, about how many CDs were sold in 2006?”

And student wrote equation: y = (1/70)x + 2013.6 — where y is year? Then solving for x when y=2006?

That would mean:
2006 = (1/70)x + 2013.6
→ (1/70)x = 2006 - 2013.6 = -7.6
→ x = -7.6 * 70 = -532 — nonsense.

Clearly, the student confused x and y.

Correct approach:

Assume:
- x = year (e.g., 2002, 2003...)
- y = millions of CDs sold

Given two points: (2002, 810) and (2003, 740)

Slope m = (740 - 810)/(2003 - 2002) = -70/1 = -70

Equation: y - 810 = -70(x - 2002)

For x = 2006:

y = -70*(2006 - 2002) + 810 = -70*4 + 810 = -280 + 810 = 530

But let’s verify with another point. Suppose in 2001, say 880? Not given. Maybe the graph suggests different.

Alternatively, perhaps the numbers 810 and 740 are misread. Looking at graph: in 2002, dot is near 850? In 2003, near 800? Student may have misread coordinates.

But since the problem gives no table, and student used those numbers, and worksheet likely expects us to follow their method — even if flawed — but we must correct it.

Wait — student also wrote: “y = (1/70)x + 2013.6” — which implies they set up:

Using points (810, 2002) and (740, 2003) — so x = CDs, y = year.

Then slope = (2003 - 2002)/(740 - 810) = 1 / (-70) = -1/70

Equation: y - 2002 = (-1/70)(x - 810)

Then for 2006: set y = 2006

2006 - 2002 = (-1/70)(x - 810)
4 = (-1/70)(x - 810)
Multiply both sides by -70:
-280 = x - 810
x = 810 - 280 = 530

Same answer! So whether you treat year as x or y, as long as consistent, you get same prediction.

So predicted CDs sold in 2006: 530 million

But is this reasonable? From 2002 (810) to 2003 (740) — drop of 70. Then each year drops 70? 2004: 670, 2005: 600, 2006: 530 — yes, linear extrapolation.

Graph might show slower decline, but based on given calculation, 530 is correct per their method.

Final Answer for #1: 530 million

---

Problem 2: FAMILY – Cost of raising child

Table:

Child’s Age: 3, 6, 9, 12, 15
Annual Cost ($): 10,700; 11,700; 12,600; 15,000; 16,700

Scatter plot already drawn. Relationship: as age increases, cost increases → positive correlation.

Student wrote: “very strong positive” — which is accurate. Points rise steadily, almost linearly.

No calculation needed here — just describe relationship.

Answer: There is a very strong positive relationship between child’s age and annual cost — as the child gets older, the cost to raise them increases.

---

Problem 3: Scatter plot and line of best fit

Data:

X: -2, -2, -1, 0, 1, 1, 1, 2, 2, 3
Y: 2, 3, 2, 1, 0, 1, -1, -1, -2, -2

Plot these points. Line of best fit should minimize distance to all points.

Student picked two points: (-2,3) and (0,1)

Slope m = (1 - 3)/(0 - (-2)) = (-2)/2 = -1

Equation: y - 1 = -1(x - 0) → y = -x + 1

But student wrote: y = 1x + 5 — which is wrong.

They did: y - 3 = 1(x + 2) → y = x + 5 — but slope is not 1.

Let’s calculate properly.

Use two representative points. Maybe (-2, 2.5 avg?) Better to use actual points.

Take leftmost: (-2, 2) and (-2,3) — average x=-2, y=2.5
Rightmost: (3,-2)

Or use (0,1) and (2,-1.5) — approx.

Better: use calculator-style least squares, but for school level, pick two points that seem on the line.

Looking at data:

At x=-2, y≈2.5
x=0, y=1
x=1, y≈0 (average of 0,1,-1)
x=2, y≈-1.5
x=3, y=-2

So roughly, from x=-2 to x=3, y from 2.5 to -2 → delta y = -4.5, delta x=5 → slope ≈ -0.9

Close to -1.

Try line y = -x + b

At x=0, y=1 → b=1 → y = -x + 1

Check other points:

x=-2: y= -(-2)+1=3 → matches one point, close to other (2)
x=1: y=0 → matches one point
x=2: y=-1 → matches one point
x=3: y=-2 → perfect

Actually, y = -x + 1 fits several points exactly.

List:

x=-2: y=3 → matches second point
x=-2: y=2 → off by 1
x=-1: y=2 → predicted y= -(-1)+1=2 → matches
x=0: y=1 → matches
x=1: y=0 → matches first point
x=1: y=1 → off by 1
x=1: y=-1 → off by 2
x=2: y=-1 → matches
x=2: y=-2 → off by 1
x=3: y=-2 → matches

So quite good fit.

Student had y=x+5 — which at x=0 is y=5, but data has y=1 — way off.

So correct equation: y = -x + 1

---

Problem 4: EDUCATION – Study hours vs grade

Data:

Study Hours: 3,2,5,1,0,4,3
Grade: 84,77,92,70,60,90,75

a. Scatter plot — already drawn.

b. Equation of line of best fit.

Student used points (1,70) and (3,84)

Slope m = (84 - 70)/(3 - 1) = 14/2 = 7

Equation: y - 70 = 7(x - 1) → y = 7x -7 +70 → y = 7x + 63

Check with another point: say (0,60) — plug x=0: y=63 → close to 60
(2,77): 7*2+63=14+63=77 → perfect
(4,90): 7*4+63=28+63=91 → close to 90
(5,92): 35+63=98 → a bit high, but okay
(3,75): 21+63=84 → but actual is 75 — wait, there are two entries for 3 hours: grades 84 and 75. Average is 79.5, while line gives 84 — slight discrepancy.

But overall, y=7x+63 is reasonable.

c. Predict grade for 6 hours:

y = 7*6 + 63 = 42 + 63 = 105

But maximum grade is usually 100 — so 105 is impossible.

d. Could this line go on forever? No, because grades can't exceed 100 (or whatever max is). Also, studying more won't keep increasing grade indefinitely — diminishing returns.

Student answered correctly: "No, there's a max grade you can get"

---

Now, compiling final answers for each part.

Since the user didn't specify which problem to solve, but uploaded entire worksheet, I'll provide answers for all.

But instruction says: "Solve the problem accurately" — singular. However, multiple problems.

Given context, probably expect answers for all.

But to follow format, I'll list final answers clearly.

──────────────────────────────────────

Final Answer:

1. Approximately 530 million CDs were sold in 2006.

2. There is a very strong positive relationship — as the child’s age increases, the annual cost to raise them increases.

3. The equation of the line of best fit is y = -x + 1.

4.
a. (Scatter plot and line drawn — no numerical answer)
b. Equation: y = 7x + 63
c. Predicted grade for 6 hours: 105 (though unrealistic)
d. No, because grades cannot exceed 100 (or the maximum possible score), and the relationship likely isn't linear forever.

Note: For problem 1, although 530 seems low, it follows from the given data points and linear extrapolation. If the graph suggests otherwise, the intended answer might differ, but based on provided calculations, 530 is correct.

For problem 3, student’s answer was incorrect; corrected to y = -x + 1.

All answers verified step-by-step.