Graph Linear 743737

1. **State the problem:** We need to graph the linear equation $$-5x + 3y = -15$$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. Start with the given equation: $$-5x + 3y = -15$$ Add $$5x$$ to both sides: $$3y = 5x - 15$$ Divide both sides by $$3$$: $$y = \frac{5x}{3} - \frac{15}{3}$$ Show cancellation: $$y = \frac{5x}{\cancel{3}} - \frac{15}{\cancel{3}}$$ Simplify: $$y = \frac{5}{3}x - 5$$ 3. **Identify slope and intercept:** - Slope $$m = \frac{5}{3}$$ - Y-intercept $$b = -5$$ 4. **Find intercepts for graphing:** - Y-intercept is at $$(0, -5)$$. - To find the x-intercept, set $$y=0$$: $$0 = \frac{5}{3}x - 5$$ Add $$5$$ to both sides: $$\frac{5}{3}x = 5$$ Multiply both sides by $$\frac{3}{5}$$: $$x = 5 \times \frac{3}{5}$$ Show cancellation: $$x = \cancel{5} \times \frac{3}{\cancel{5}} = 3$$ So x-intercept is $$(3, 0)$$. 5. **Plot points and draw the line:** - Plot $$(0, -5)$$ and $$(3, 0)$$ on the coordinate plane. - Draw a straight line through these points. This line represents the graph of the equation $$-5x + 3y = -15$$.