1. Problem: Convert each given linear equation to slope-intercept form $y = mx + b$ and interpret the slope and intercept. 2. For $11\ 2x = \frac{5x - 2y}{4}$: Multiply both sides by 4: $8x = 5x - 2y$ Rearrange: $8x - 5x = -2y \Rightarrow 3x = -2y$ Divide by -2: $y = -\frac{3}{2}x$ Slope $m = -\frac{3}{2}$, intercept $b=0$. 3. For $13\ 4x - 3y = 0$: Rearrange: $-3y = -4x \Rightarrow y = \frac{4}{3}x$ Slope $m=\frac{4}{3}$, intercept $b=0$. 4. For $15\ 3x - 6y + 10 = x$: Simplify: $3x - 6y + 10 = x \Rightarrow 3x - x - 6y + 10 = 0 \Rightarrow 2x - 6y + 10 = 0$ Rearrange: $-6y = -2x - 10 \Rightarrow y = \frac{1}{3}x + \frac{5}{3}$ Slope $m=\frac{1}{3}$, intercept $b=\frac{5}{3}$. 5. For $17\ 2x + 3y = 4x + 3y$: Subtract $3y$ both sides: $2x = 4x$ Simplify: $2x - 4x = 0 \Rightarrow -2x = 0 \Rightarrow x=0$ Vertical line $x=0$, slope undefined. 6. For $19\ 8y - 24 = 0$: Rearrange: $8y = 24 \Rightarrow y = 3$ Horizontal line $y=3$, slope $m=0$, intercept $b=3$. 7. For $21\ mx + ny = p$: Solve for $y$: $ny = p - mx \Rightarrow y = -\frac{m}{n}x + \frac{p}{n}$ Slope $m = -\frac{m}{n}$, intercept $b=\frac{p}{n}$. 8. For $23\ c - dy = 0$: Rearrange: $dy = c \Rightarrow y = \frac{c}{d}$ Horizontal line $y=\frac{c}{d}$, slope $m=0$, intercept $b=\frac{c}{d}$. 9. Women in the Labor Force: $n = 29.6 + 1.20t$ (a) Graph is a line with slope 1.20 and intercept 29.6. (b) Slope $m=1.20$, intercept $b=29.6$. (c) Slope means number of women increases by 1.20 million per year since 1981; intercept means 29.6 million women in 1981. (d) For 1995 ($t=14$): $n=29.6 + 1.20 \times 14 = 29.6 + 16.8 = 46.4$ million. For 2000 ($t=19$): $n=29.6 + 1.20 \times 19 = 29.6 + 22.8 = 52.4$ million. 10. Tourists: $p = 275000 + 7500t$ (a) Graph is a line with slope 7500 and intercept 275000. (b) Slope $m=7500$, intercept $b=275000$. (c) Slope means 7500 more tourists each year; intercept means 275000 tourists this season. 11. Temperature: $C = \frac{F - 32}{1.8}$ (a) Slope $m=\frac{1}{1.8} \approx 0.555$, intercept $b= -\frac{32}{1.8} \approx -17.78$. (b) Slope converts Fahrenheit degree changes to Celsius; intercept is Celsius at 0°F. (c) Solve for $F$: $F = 1.8C + 32$. Slope $m=1.8$, intercept $b=32$ when $F$ is vertical axis. 12. Crimes: $c = 1200 - 12.5p$ (a) Slope $m=-12.5$, meaning each additional officer reduces crimes by 12.5. (b) Intercept $b=1200$, crimes with zero officers. (c) $p$ intercept: set $c=0$, $0=1200 - 12.5p \Rightarrow p=96$ officers to reduce crimes to zero. 13. Machine value: $V = 60000 - 7500t$ Slope $m=-7500$, value decreases by 7500 per year. Intercept $b=60000$, initial value at $t=0$. Final answers are the slope-intercept forms and interpretations as above.