1. **State the problem:** We are given the formula for simple interest: $$P = H(1 + r t)$$ where $P$ is the total amount, $H$ is the principal, $r$ is the interest rate per time period, and $t$ is the time. 2. **Given values:** - Total amount $P = 1507.50$ - Principal $H = 1500$ - We want to find the interest rate $r$ or time $t$ depending on the question. 3. **Use the formula:** $$1507.50 = 1500(1 + r t)$$ 4. **Simplify:** Divide both sides by 1500: $$\frac{1507.50}{1500} = 1 + r t$$ $$1.005 = 1 + r t$$ 5. **Solve for $r t$:** $$r t = 1.005 - 1 = 0.005$$ 6. **Interpretation:** The product of the interest rate and time is 0.005, meaning the interest earned is 0.5% of the principal. --- 7. **For the linear equation $y = 2.5x + 3$:** - This is a straight line with slope 2.5 and y-intercept 3. - The slope 2.5 means for every increase of 1 in $x$, $y$ increases by 2.5. 8. **Summary:** - The interest calculation shows how to find the interest rate or time given the total amount and principal. - The linear equation describes a line with slope 2.5 and intercept 3. **Final answers:** - $r t = 0.005$ - Linear function: $y = 2.5x + 3$