Subjects algebra

Cellphones Work

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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