Subjects algebra

Y Intercept Comparison 2543C1

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1. **State the problem:** We are given two functions, Function A (a linear function graphed) and Function B (given as a table of points). We need to determine which statement about their y-intercepts is true. 2. **Identify the y-intercept of Function A:** The graph of Function A passes through approximately (0,1) on the y-axis. The y-intercept is the value of $y$ when $x=0$, so for Function A, $y=1$. 3. **Find the y-intercept of Function B:** Function B is given by points $(-4,-7)$, $(-1,-1)$, and $(5,11)$. To find the y-intercept, we need the equation of the line passing through these points. 4. **Calculate the slope $m$ of Function B:** Using points $(-4,-7)$ and $(-1,-1)$, $$m=\frac{-1 - (-7)}{-1 - (-4)}=\frac{6}{3}=2$$ 5. **Find the equation of Function B:** Using point-slope form with point $(-1,-1)$, $$y - (-1) = 2(x - (-1))$$ $$y + 1 = 2(x + 1)$$ $$y + 1 = 2x + 2$$ $$y = 2x + 1$$ 6. **Find the y-intercept of Function B:** Set $x=0$, $$y = 2(0) + 1 = 1$$ 7. **Compare y-intercepts:** Function A has y-intercept $1$, Function B has y-intercept $1$. 8. **Conclusion:** The y-intercepts are equal, so neither statement "The y-intercept of Function A is greater than Function B" nor "less than" is true based on the given data. **Final answer:** The y-intercepts of Function A and Function B are equal at $y=1$.