Question

Can someone help me please? It’s like my 3rd time trying to get some answers for this question. Thanks. :)

Answer 1

Answer:

both rates of change equal the slope of the line (3/4)

Step-by-step explanation:

Part a)

We calculate the rate of change using the formula:

$\frac{y_2-y_1}{x_2-x_1}$

for the first interval [0,6], we calculate the y-values at x=0 and x=6;

at x=0 : $y=\frac{3}{2} (0)+2=2$

at x=6 : $y=\frac{3}{2} (6)+2=11$

therefore, the rate of change in this interval is: $\frac{y_2-y_1}{x_2-x_1}=\frac{11-2}{6-0}=\frac{9}{6} =\frac{3}{2}$

For the second interval [-4,4], we calculate the y-values at x=-4 and x=4;

at x=-4 : $y=\frac{3}{2} (-4)+2=-4$

at x=4 : $y=\frac{3}{2} (4)+2=8$

therefore, the rate of change in this interval is: $\frac{y_2-y_1}{x_2-x_1}=\frac{8-(-4)}{4-(-4)}=\frac{12}{8} =\frac{3}{2}$

Part b):

Notice that both rates of change equal the value of the slope of the linear function (3/2)