Subjects algebra

Slope Comparison 8252Ef

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1. The problem asks us to compare the slopes of two functions, Function A and Function B, based on given points and a graph description. 2. The slope formula for a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is: $$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. For Function A, we have points $(-4,-10)$ and $(-1,-1)$. Calculate the slope: $$m_A = \frac{-1 - (-10)}{-1 - (-4)} = \frac{-1 + 10}{-1 + 4} = \frac{9}{3} = 3$$ 4. For Function B, the graph shows a line increasing from approximately $(0,-10)$ to $(2,10)$. Calculate the slope: $$m_B = \frac{10 - (-10)}{2 - 0} = \frac{10 + 10}{2} = \frac{20}{2} = 10$$ 5. Compare the slopes: $$m_A = 3 < m_B = 10$$ 6. Therefore, the slope of Function A is less than the slope of Function B. Final answer: The slope of Function A is less than the slope of Function B.