Graph Equation 142De3

1. **State the problem:** We need to graph the linear equation $$3x + 5y = 30$$. 2. **Rewrite the equation in slope-intercept form:** To graph easily, solve for $y$: $$3x + 5y = 30$$ Subtract $3x$ from both sides: $$5y = 30 - 3x$$ Divide both sides by $5$: $$y = \frac{30 - 3x}{5}$$ Show cancellation: $$y = \frac{\cancel{30} - 3x}{\cancel{5}}$$ Simplify: $$y = 6 - \frac{3}{5}x$$ 3. **Identify slope and intercept:** - Slope $m = -\frac{3}{5}$ - $y$-intercept $b = 6$ 4. **Find intercepts:** - $y$-intercept: When $x=0$, $y=6$. - $x$-intercept: When $y=0$, solve $3x + 5(0) = 30 \Rightarrow 3x=30 \Rightarrow x=10$. 5. **Plot points:** - Plot $(0,6)$ on the $y$-axis. - Plot $(10,0)$ on the $x$-axis. 6. **Draw the line:** Connect these two points with a straight line. This is the graph of the equation. **Final answer:** The graph is a straight line passing through points $(0,6)$ and $(10,0)$ with slope $-\frac{3}{5}$.