1. **State the problem:** We have two points representing the number of drills sold and their prices: $(3000, 70)$ and $(4000, 60)$. We want to find the slope of the line between these points, interpret it, and use it to predict the number of drills sold at a price of $64$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ This slope represents the rate of change of price with respect to the number of drills sold. 3. **Calculate the slope:** $$m = \frac{60 - 70}{4000 - 3000} = \frac{-10}{1000} = -0.01$$ This means the price decreases by $0.01$ dollars for each additional drill sold. 4. **Interpretation:** For every additional drill sold, the price per drill decreases by $0.01$ dollars, which is equivalent to 1 cent. 5. **Find the number of drills sold at $64$ dollars:** Use the point-slope form of the line: $$y - y_1 = m(x - x_1)$$ Substitute $y = 64$, $m = -0.01$, and point $(3000, 70)$: $$64 - 70 = -0.01(x - 3000)$$ $$-6 = -0.01x + 30$$ $$-6 - 30 = -0.01x$$ $$-36 = -0.01x$$ $$x = \frac{36}{0.01} = 3600$$ **Final answer:** (a) The slope is $-0.01$. (b) For every additional drill sold, the price per drill decreases by 1 cent. (c) At a price of $64$, 3600 drills can be sold.