1. **State the problem:** We need to graph the two linear equations: $$y = -2x - 3$$ and $$y = \frac{3}{2}x + 4$$ on the coordinate plane. 2. **Recall the slope-intercept form:** The general form of a linear equation is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slopes and intercepts:** - For $$y = -2x - 3$$, the slope $m = -2$ and the y-intercept $b = -3$. - For $$y = \frac{3}{2}x + 4$$, the slope $m = \frac{3}{2}$ and the y-intercept $b = 4$. 4. **Plot the y-intercepts:** - Plot the point $(0, -3)$ for the first line. - Plot the point $(0, 4)$ for the second line. 5. **Use the slope to find another point:** - For the first line, slope $-2$ means go down 2 units and right 1 unit from $(0, -3)$ to get $(1, -5)$. - For the second line, slope $\frac{3}{2}$ means go up 3 units and right 2 units from $(0, 4)$ to get $(2, 7)$. 6. **Draw the lines:** Connect the points for each line extending in both directions. **Final answer:** The two lines are graphed with their respective slopes and intercepts as described.