1. **State the problem:** We need to find the equations of lines parallel to given lines (Line 1, Line 2, Line 3) passing through specific points (4,7), (9,6), and (-3,12). 2. **Recall the formula:** The equation of a line in slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Important rule for parallel lines:** Parallel lines have the same slope $m$ but different y-intercepts $b$. 4. **Line 7:** Parallel to Line 1 with slope $m = -\frac{5}{4}$, passing through $(4,7)$. Use point-slope form: $$y = mx + b \Rightarrow 7 = -\frac{5}{4} \times 4 + b$$ Calculate: $$7 = -5 + b$$ Add 5 to both sides: $$7 + 5 = b \Rightarrow b = 12$$ Equation: $$y = -\frac{5}{4}x + 12$$ 5. **Line 8:** Parallel to Line 2 with slope $m = 4$, passing through $(9,6)$. Use point-slope form: $$6 = 4 \times 9 + b$$ Calculate: $$6 = 36 + b$$ Subtract 36 from both sides: $$6 - 36 = b \Rightarrow b = -30$$ Equation: $$y = 4x - 30$$ 6. **Line 9:** Parallel to Line 3 with slope $m = \frac{2}{3}$, passing through $(-3,12)$. Use point-slope form: $$12 = \frac{2}{3} \times (-3) + b$$ Calculate: $$12 = -2 + b$$ Add 2 to both sides: $$12 + 2 = b \Rightarrow b = 14$$ Equation: $$y = \frac{2}{3}x + 14$$ **Final answers:** - Line 7: $$y = -\frac{5}{4}x + 12$$ - Line 8: $$y = 4x - 30$$ - Line 9: $$y = \frac{2}{3}x + 14$$