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:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
for the first interval [0,6], we calculate the y-values at x=0 and x=6;
at x=0 : [tex]y=\frac{3}{2} (0)+2=2[/tex]
at x=6 : [tex]y=\frac{3}{2} (6)+2=11[/tex]
therefore, the rate of change in this interval is: [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{11-2}{6-0}=\frac{9}{6} =\frac{3}{2}[/tex]
For the second interval [-4,4], we calculate the y-values at x=-4 and x=4;
at x=-4 : [tex]y=\frac{3}{2} (-4)+2=-4[/tex]
at x=4 : [tex]y=\frac{3}{2} (4)+2=8[/tex]
therefore, the rate of change in this interval is: [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{8-(-4)}{4-(-4)}=\frac{12}{8} =\frac{3}{2}[/tex]
Part b):
Notice that both rates of change equal the value of the slope of the linear function (3/2)
