Question: help me solve $(3x+y=9)$ graphing equations
1. **State the problem:** We need to graph the equation $$3x + y = 9$$.
2. **Rewrite the equation in slope-intercept form:** To graph easily, solve for $y$:
$$3x + y = 9$$
Subtract $3x$ from both sides:
$$y = 9 - 3x$$
3. **Identify slope and intercept:** The equation is now in the form $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept.
Here, $m = -3$ and $b = 9$.
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.
This line represents all solutions to the equation $3x + y = 9$.