Subjects algebra

Line Best Fit 83575C

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1. **State the problem:** We are given the equation of the line of best fit: $$y = \frac{1}{20}x + 7$$ where $y$ represents the cost in dollars and $x$ represents the number of pencils. 2. **Understand the slope and intercept:** The equation is in slope-intercept form $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Interpret the slope:** The slope $m = \frac{1}{20}$ means that for every increase of 1 pencil, the cost increases by $\frac{1}{20}$ dollars. 4. **Calculate cost increase for 20 pencils:** For 20 pencils, the increase in cost is $$\frac{1}{20} \times 20 = 1$$ dollar. 5. **Interpret the y-intercept:** The y-intercept $b = 7$ means that when there are 0 pencils, the cost is 7 dollars (possibly a base cost). 6. **Answer the question:** The correct statement is: "For every 20 additional pencils in a package, the cost increases by about 1." This is because the slope tells us the cost increase per pencil, and multiplying by 20 pencils gives an increase of 1 dollar. **Final answer:** For every 20 additional pencils in a package, the cost increases by about 1.