1. **State the problem:** Solve the system of equations by graphing: $$y = 3x - 2$$ $$y = -x + 6$$ Find the point where the two lines intersect. 2. **Graph each equation:** - For $$y = 3x - 2$$, the slope is 3 and the y-intercept is -2. - For $$y = -x + 6$$, the slope is -1 and the y-intercept is 6. 3. **Find the intersection point algebraically:** Set the right sides equal since both equal $$y$$: $$3x - 2 = -x + 6$$ 4. **Solve for $$x$$:** $$3x + x = 6 + 2$$ $$4x = 8$$ $$x = 2$$ 5. **Find $$y$$ by substituting $$x=2$$ into one of the equations:** $$y = 3(2) - 2 = 6 - 2 = 4$$ 6. **Solution:** The lines intersect at the point $$(2, 4)$$. --- **How to graph linear and quadratic functions:** - **Linear function:** Plot the y-intercept on the y-axis, then use the slope to find another point (rise over run). Draw a straight line through these points. - **Quadratic function:** Identify the vertex (highest or lowest point), plot it. Find additional points by substituting x-values into the equation. Draw a smooth curve through these points forming a parabola.