1. **State the problem:** We are analyzing a linear relationship between the number of cellphones confiscated (x) and the minutes of work done (y).
2. **Given data points:** (0, 3) and (4, 6).
3. **Label axes:** x-axis is "Number of Cellphones" and y-axis is "Minutes of Work".
4. **Find the slope (m):** Use the formula $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 3}{4 - 0} = \frac{3}{4}$$.
5. **Find the y-intercept (b):** Since the line passes through (0, 3), the y-intercept is 3.
6. **Equation of the line:** Using slope-intercept form $$y = mx + b$$, we get $$y = \frac{3}{4}x + 3$$.
7. **Calculate minutes of work if 2 cellphones are confiscated:** Substitute $x=2$ into the equation:
$$y = \frac{3}{4} \times 2 + 3 = \frac{3}{2} + 3 = 4.5$$ minutes.
8. **Calculate number of cellphones to get 20 minutes of work:** Set $y=20$ and solve for $x$:
$$20 = \frac{3}{4}x + 3$$
$$20 - 3 = \frac{3}{4}x$$
$$17 = \frac{3}{4}x$$
$$x = \frac{17 \times 4}{3} = \frac{68}{3} \approx 22.67$$
So, approximately 23 cellphones need to be confiscated.
9. **Calculate minutes of work if all 24 cellphones are confiscated:** Substitute $x=24$:
$$y = \frac{3}{4} \times 24 + 3 = 18 + 3 = 21$$ minutes.
**Note:** The user’s answers for parts d, e, and g differ slightly from calculations; the correct values based on the equation are shown here.
Final answers:
- Equation: $$y = \frac{3}{4}x + 3$$
- Minutes for 2 cellphones: 4.5
- Cellphones for 20 minutes: approximately 23
- Minutes for 24 cellphones: 21
Cellphones Work
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