1. **Problem Statement:** Complete the table for the graph of $$y=\frac{3x-2}{2}$$ and draw the graph of $$y=\frac{3}{2}x - 1$$. 2. **Formula and Rules:** The equation is linear in the form $$y=mx+c$$ where $$m$$ is the slope and $$c$$ is the y-intercept. 3. **Complete the table:** Given $$y=\frac{3x-2}{2}$$, calculate $$y$$ for each $$x$$: - For $$x=-4$$: $$y=\frac{3(-4)-2}{2}=\frac{-12-2}{2}=\frac{-14}{2}=-7$$ - For $$x=0$$: $$y=\frac{3(0)-2}{2}=\frac{-2}{2}=-1$$ - For $$x=2$$: $$y=\frac{3(2)-2}{2}=\frac{6-2}{2}=\frac{4}{2}=2$$ - For $$x=6$$: $$y=\frac{3(6)-2}{2}=\frac{18-2}{2}=\frac{16}{2}=8$$ 4. **Graph equation:** Rewrite $$y=\frac{3x-2}{2}$$ as $$y=\frac{3}{2}x - 1$$. 5. **Calculate slope:** The slope $$m=\frac{3}{2}$$. 6. **Second line:** Equation with slope $$\frac{2}{5}$$ passing through $$(3,-2)$$ is: $$y - (-2) = \frac{2}{5}(x - 3)$$ $$y + 2 = \frac{2}{5}x - \frac{6}{5}$$ $$y = \frac{2}{5}x - \frac{6}{5} - 2 = \frac{2}{5}x - \frac{16}{5}$$ 7. **Find intersection:** Set the two equations equal: $$\frac{3}{2}x - 1 = \frac{2}{5}x - \frac{16}{5}$$ Multiply both sides by 10 to clear denominators: $$10 \times \left(\frac{3}{2}x - 1\right) = 10 \times \left(\frac{2}{5}x - \frac{16}{5}\right)$$ $$15x - 10 = 4x - 32$$ Subtract $$4x$$ from both sides: $$15x - \cancel{4x} - 10 = \cancel{4x} - 32$$ $$11x - 10 = -32$$ Add 10 to both sides: $$11x = -22$$ Divide both sides by 11: $$x = \frac{-22}{11} = -2$$ Substitute $$x=-2$$ into first equation: $$y = \frac{3}{2}(-2) - 1 = -3 - 1 = -4$$ **Intersection point:** $$(-2, -4)$$