Subjects algebra

Compare Slopes D0394C

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1. **State the problem:** We are given two linear functions, Function A and Function B, and need to determine which has the greater slope. 2. **Recall the slope formula:** For any two points $(x_1,y_1)$ and $(x_2,y_2)$ on a line, the slope $m$ is given by: $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope of Function A:** Using points $(-6,-8)$ and $(3,1)$: $$m_A=\frac{1 - (-8)}{3 - (-6)}=\frac{1 + 8}{3 + 6}=\frac{9}{9}=1$$ 4. **Calculate the slope of Function B:** The graph passes through approximately $(-10,0)$ and $(10,6)$: $$m_B=\frac{6 - 0}{10 - (-10)}=\frac{6}{20}=\frac{3}{10}=0.3$$ 5. **Compare slopes:** $$m_A=1 > m_B=0.3$$ 6. **Conclusion:** The slope of Function A is greater than the slope of Function B.