Graph Equation B90B00

1. **State the problem:** We need to graph the linear equation $$5x + 6y = 30$$. 2. **Rewrite the equation in slope-intercept form:** To graph easily, solve for $y$: $$5x + 6y = 30$$ Subtract $5x$ from both sides: $$6y = 30 - 5x$$ Divide both sides by $6$: $$y = \frac{30 - 5x}{6}$$ Use \cancel to show division: $$y = \frac{\cancel{30} - 5x}{\cancel{6}}$$ (simplify later) Simplify the fraction: $$y = 5 - \frac{5}{6}x$$ 3. **Identify slope and intercept:** - Slope $m = -\frac{5}{6}$ - Y-intercept $b = 5$ 4. **Find intercepts:** - When $x=0$, $y=5$ (y-intercept) - When $y=0$, solve $5x + 6(0) = 30$: $$5x = 30$$ $$x = \frac{30}{5} = 6$$ So x-intercept is $(6,0)$. 5. **Plot points and draw line:** Plot points $(0,5)$ and $(6,0)$ on the coordinate plane and draw a straight line through them. This line represents the graph of the equation $5x + 6y = 30$.