1. **Problem 32:** Find the equation of the linear relationship between sales $x$ and selling expense $y$ when sales increase from 100 to 400 and expense from 75 to 150. 2. **Calculate the slope $m$** using the formula for slope between two points: $$m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{150 - 75}{400 - 100}=\frac{75}{300}=0.25$$ 3. **Use point-slope form** of a line equation with point (100, 75): $$y - 75 = 0.25(x - 100)$$ 4. **Simplify to slope-intercept form $y=mx+b$:$$y - 75 = 0.25x - 25$$ $$y=0.25x - 25 + 75 = 0.25x + 50$$ 5. **Conclusion:** The equation relating selling expense $y$ to sales $x$ is $$y=0.25x + 50$$ which means for each additional unit of sales, selling expense increases by 0.25, starting from a base expense of 50 when sales are zero.