Subjects algebra

Line Graph Aebdf0

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1. **State the problem:** We need to graph the line given by the equation $$y=\frac{2}{5}x+1$$ and list two points on the line, then describe the rise/run between those points. 2. **Formula and explanation:** The equation is in slope-intercept form $$y=mx+b$$ where $$m=\frac{2}{5}$$ is the slope and $$b=1$$ is the y-intercept. 3. **Find the y-intercept point:** When $$x=0$$, $$y=\frac{2}{5}\times0+1=1$$, so the point is $$(0,1)$$. 4. **Find a second point using the slope:** The slope $$m=\frac{2}{5}$$ means "rise over run" = rise of 2 units for every run of 5 units. Starting from $$(0,1)$$, move right 5 units: $$x=0+5=5$$. Calculate $$y$$ at $$x=5$$: $$y=\frac{2}{5}\times5+1=2+1=3$$. So the second point is $$(5,3)$$. 5. **Describe the rise/run:** Between points $$(0,1)$$ and $$(5,3)$$, the rise is $$3-1=2$$ and the run is $$5-0=5$$. This matches the slope $$\frac{2}{5}$$. **Final answer:** Two points to plot are $$(0,1)$$ and $$(5,3)$$. The rise/run between these points is rise = 2 and run = 5.