Graph Intercepts D6495B

1. **State the problem:** Find the intercepts of the graph of the linear equation $$y=3x+2$$. 2. **Recall the intercepts:** - The **y-intercept** is the point where the graph crosses the y-axis, which happens when $$x=0$$. - The **x-intercept** is the point where the graph crosses the x-axis, which happens when $$y=0$$. 3. **Find the y-intercept:** Substitute $$x=0$$ into the equation: $$y=3(0)+2=2$$ So the y-intercept is at the point $$(0,2)$$. 4. **Find the x-intercept:** Set $$y=0$$ and solve for $$x$$: $$0=3x+2$$ $$3x=-2$$ $$x=\frac{-2}{3}$$ 5. **Simplify and show cancellation:** $$x=\frac{\cancel{3} \times (-\frac{2}{3})}{\cancel{3}} = -\frac{2}{3}$$ 6. **Conclusion:** - The y-intercept is $$(0,2)$$. - The x-intercept is $$\left(-\frac{2}{3},0\right)$$.