Subjects algebra

Linear Predictions

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1. **Problem 25:** Given the linear equation $$n = 29.6 + 1.20t$$ where $$n$$ is the number of women (in millions) aged 35 to 44 in the labor force and $$t$$ is years since 1981. 2. **Graph the equation:** This is a straight line with slope 1.20 and y-intercept 29.6. 3. **Identify slope and intercept:** Slope $$m = 1.20$$, y-intercept $$b = 29.6$$. 4. **Interpret slope and intercept:** - Slope 1.20 means the number of women in the labor force increases by 1.20 million each year after 1981. - Intercept 29.6 means in 1981 ($$t=0$$), there were 29.6 million women in the labor force aged 35 to 44. 5. **Predict number in 1995:** $$t = 1995 - 1981 = 14$$ $$n = 29.6 + 1.20 \times 14 = 29.6 + 16.8 = 46.4$$ million. 6. **Predict number in 2000:** $$t = 2000 - 1981 = 19$$ $$n = 29.6 + 1.20 \times 19 = 29.6 + 22.8 = 52.4$$ million. 7. **Problem 26:** Given the linear equation $$p = 275000 + 7500t$$ where $$p$$ is the number of tourists per year and $$t$$ is years from current season. 8. **Graph the equation:** This is a straight line with slope 7500 and y-intercept 275000. 9. **Identify slope and intercept:** Slope $$m = 7500$$, y-intercept $$b = 275000$$. 10. **Interpret slope and intercept:** - Slope 7500 means the number of tourists increases by 7500 each year. - Intercept 275000 means currently ($$t=0$$) there are 275000 tourists.