1. **State the problem:** We have two functions, Function A represented by the table of values and Function B represented by the equation $y=\frac{3}{2}x+2$. We need to find the rate of change and initial value for each and compare them. 2. **Rate of change from the table (Function A):** The rate of change is the change in $y$ divided by the change in $x$ between two points. Calculate between points $(-2,-7)$ and $(0,-2)$: $$\text{Rate} = \frac{-2 - (-7)}{0 - (-2)} = \frac{5}{2} = 2.5$$ Check between $(0,-2)$ and $(6,13)$: $$\frac{13 - (-2)}{6 - 0} = \frac{15}{6} = 2.5$$ Check between $(6,13)$ and $(12,28)$: $$\frac{28 - 13}{12 - 6} = \frac{15}{6} = 2.5$$ So, the rate of change for Function A is $2.5$. 3. **Initial value from the table (Function A):** The initial value is the $y$-value when $x=0$. From the table, when $x=0$, $y=-2$. So, initial value is $-2$. 4. **Rate of change from the equation (Function B):** The equation is $y=\frac{3}{2}x+2$. The rate of change is the coefficient of $x$, which is $\frac{3}{2} = 1.5$. 5. **Initial value from the equation (Function B):** The initial value is the constant term, which is $2$. 6. **Compare initial values:** - Function A initial value: $-2$ - Function B initial value: $2$ Since $-2 < 2$, the initial value of Function A is less than that of Function B. 7. **Compare rates of change:** - Function A rate: $2.5$ - Function B rate: $1.5$ Since $2.5 > 1.5$, the rate of change of Function A is greater than that of Function B. 8. **Regarding initial values:** - Only Function A has a negative initial value. 9. **Regarding rates of change:** - Neither rate of change is negative (both are positive). **Final answers:** - Rate of change in the table (Function A): $2.5$ - Initial value in the table (Function A): $-2$ - Rate of change in the equation (Function B): $1.5$ - Initial value in the equation (Function B): $2$ - True statements: - The initial value of Function A is less than the initial value of Function B. - The rate of change of Function A is greater than the rate of change of Function B. - Only Function A has a negative initial value. - Neither rate of change is negative.