Subjects algebra

Compare Functions 8Ab3Cc

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1. The problem asks to compare the y-intercepts and rates of change of two functions. 2. The first function is given as $y = 6x - 1$. 3. The second function (II) is described by points: $(0, -1), (1, 0), (2, 1), (3, 2), (4, 3)$. 4. The y-intercept is the value of $y$ when $x=0$. 5. For the first function, the y-intercept is $-1$ (from $y=6(0)-1=-1$). 6. For the second function, the y-intercept is also $-1$ (point $(0,-1)$). 7. The rate of change (slope) is calculated by the change in $y$ over the change in $x$. 8. For the first function, the slope is $6$ (coefficient of $x$). 9. For the second function, calculate slope between two points, for example between $(0,-1)$ and $(1,0)$: $$\text{slope} = \frac{0 - (-1)}{1 - 0} = \frac{1}{1} = 1$$ 10. Since the slopes are different ($6$ vs $1$) but the y-intercepts are the same ($-1$), the correct comparison is: **C. The y-intercepts are the same, but the rates of change are different.**