Graphing Equation D65818

1. **State the problem:** We need to graph the linear equation $$3x + y = 9$$. 2. **Rewrite the equation in slope-intercept form:** To graph easily, solve for $y$: $$3x + y = 9$$ $$y = 9 - 3x$$ 3. **Identify slope and intercept:** The equation is now in the form $$y = mx + b$$ where $$m = -3$$ (slope) and $$b = 9$$ (y-intercept). 4. **Plot the y-intercept:** Start by plotting the point $(0, 9)$ on the y-axis. 5. **Use the slope to find another point:** The slope $$-3$$ means for every 1 unit increase in $x$, $y$ decreases by 3 units. From $(0,9)$, move right 1 unit to $x=1$, then down 3 units to $y=6$. Plot $(1,6)$. 6. **Draw the line:** Connect the points $(0,9)$ and $(1,6)$ with a straight line extending in both directions. 7. **Check intercepts:** - When $x=0$, $y=9$ (already plotted). - When $y=0$, solve $3x + 0 = 9$ so $x=3$. Plot $(3,0)$. This confirms the line passes through $(0,9)$ and $(3,0)$. **Final answer:** The graph of $$3x + y = 9$$ is a straight line crossing the y-axis at 9 and the x-axis at 3.